TOC of Theorem List - Intuitionistic Logic Explorer

Table of Contents Summary

PART 1  INTUITIONISTIC FIRST-ORDER LOGIC WITH EQUALITY
      1.1  Pre-logic
      1.2  Propositional calculus
      1.3  Predicate calculus mostly without distinct variables
      1.4  Predicate calculus with distinct variables
      1.5  First-order logic with one non-logical binary predicate
PART 2  SET THEORY
      2.1  IZF Set Theory - start with the Axiom of Extensionality
      2.2  IZF Set Theory - add the Axioms of Collection and Separation
      2.3  IZF Set Theory - add the Axioms of Power Sets and Pairing
      2.4  IZF Set Theory - add the Axiom of Union
      2.5  IZF Set Theory - add the Axiom of Set Induction
      2.6  IZF Set Theory - add the Axiom of Infinity
PART 3  CHOICE PRINCIPLES
      3.1  Countable Choice and Dependent Choice
PART 4  REAL AND COMPLEX NUMBERS
      4.1  Construction and axiomatization of real and complex numbers
      4.2  Derive the basic properties from the field axioms
      4.3  Real and complex numbers - basic operations
      4.4  Integer sets
      4.5  Order sets
      4.6  Elementary integer functions
      4.7  Elementary real and complex functions
      4.8  Elementary limits and convergence
      4.9  Elementary trigonometry
PART 5  ELEMENTARY NUMBER THEORY
      5.1  Elementary properties of divisibility
      5.2  Elementary prime number theory
      5.3  Cardinality of real and complex number subsets
PART 6  BASIC STRUCTURES
      6.1  Extensible structures
PART 7  BASIC ALGEBRAIC STRUCTURES
      7.1  Monoids
      7.2  Groups
      7.3  Rings
      7.4  Division rings and fields
      7.5  Left modules
      7.6  Subring algebras and ideals
      7.7  The complex numbers as an algebraic extensible structure
PART 8  BASIC TOPOLOGY
      8.1  Topology
      8.2  Metric spaces
PART 9  BASIC REAL AND COMPLEX ANALYSIS
      9.1  Derivatives
PART 10  BASIC REAL AND COMPLEX FUNCTIONS
      10.1  Basic trigonometry
      10.2  Basic number theory
PART 11  GUIDES AND MISCELLANEA
      11.1  Guides (conventions, explanations, and examples)
PART 12  SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
      ​12.1  Mathboxes for user contributions
      12.2  Mathbox for BJ
      12.3  Mathbox for Jim Kingdon
      12.4  Mathbox for Mykola Mostovenko
      12.5  Mathbox for David A. Wheeler

Detailed Table of Contents
(* means the section header has a description)

​​*PART 1  INTUITIONISTIC FIRST-ORDER LOGIC WITH EQUALITY
      ​*1.1  Pre-logic
            *1.1.1  Inferences for assisting proof development   idi 1
      ​​*1.2  Propositional calculus
            1.2.1  Recursively define primitive wffs for propositional calculus   wn 3
            1.2.2  Propositional logic axioms for implication   ax-mp 5
            ​*1.2.3  Logical implication   mp2b 8
            1.2.4  Logical conjunction and logical equivalence   wa 104
            1.2.5  Logical negation (intuitionistic)   ax-in1 615
            1.2.6  Logical disjunction   wo 709
            1.2.7  Stable propositions   wstab 831
            1.2.8  Decidable propositions   wdc 835
            ​*1.2.9  Theorems of decidable propositions   const 853
            1.2.10  Miscellaneous theorems of propositional calculus   pm5.21nd 917
            1.2.11  Abbreviated conjunction and disjunction of three wff's   w3o 978
            1.2.12  True and false constants   wal 1361
                  ​*1.2.12.1  Universal quantifier for use by df-tru   wal 1361
                  ​*1.2.12.2  Equality predicate for use by df-tru   cv 1362
                  1.2.12.3  Define the true and false constants   wtru 1364
            1.2.13  Logical 'xor'   wxo 1385
            ​*1.2.14  Truth tables: Operations on true and false constants   truantru 1411
            ​*1.2.15  Stoic logic indemonstrables (Chrysippus of Soli)   mptnan 1433
            1.2.16  Logical implication (continued)   syl6an 1444
      ​1.3  Predicate calculus mostly without distinct variables
            ​*1.3.1  Universal quantifier (continued)   ax-5 1457
            ​*1.3.2  Equality predicate (continued)   weq 1513
            1.3.3  Axiom ax-17 - first use of the $d distinct variable statement   ax-17 1536
            1.3.4  Introduce Axiom of Existence   ax-i9 1540
            1.3.5  Additional intuitionistic axioms   ax-ial 1544
            1.3.6  Predicate calculus including ax-4, without distinct variables   spi 1546
            1.3.7  The existential quantifier   19.8a 1600
            1.3.8  Equality theorems without distinct variables   a9e 1706
            1.3.9  Axioms ax-10 and ax-11   ax10o 1725
            1.3.10  Substitution (without distinct variables)   wsb 1772
            1.3.11  Theorems using axiom ax-11   equs5a 1804
      ​1.4  Predicate calculus with distinct variables
            1.4.1  Derive the axiom of distinct variables ax-16   spimv 1821
            1.4.2  Derive the obsolete axiom of variable substitution ax-11o   ax11o 1832
            1.4.3  More theorems related to ax-11 and substitution   albidv 1834
            1.4.4  Predicate calculus with distinct variables (cont.)   ax16i 1868
            1.4.5  More substitution theorems   hbs1 1948
            1.4.6  Existential uniqueness   weu 2036
            ​*1.4.7  Aristotelian logic: Assertic syllogisms   barbara 2134
      ​​*1.5  First-order logic with one non-logical binary predicate
​​*PART 2  SET THEORY
      ​2.1  IZF Set Theory - start with the Axiom of Extensionality
            2.1.1  Introduce the Axiom of Extensionality   ax-ext 2169
            2.1.2  Class abstractions (a.k.a. class builders)   cab 2173
            2.1.3  Class form not-free predicate   wnfc 2316
            2.1.4  Negated equality and membership   wne 2357
                  2.1.4.1  Negated equality   wne 2357
                  2.1.4.2  Negated membership   wnel 2452
            2.1.5  Restricted quantification   wral 2465
            2.1.6  The universal class   cvv 2749
            ​*2.1.7  Conditional equality (experimental)   wcdeq 2957
            2.1.8  Russell's Paradox   ru 2973
            2.1.9  Proper substitution of classes for sets   wsbc 2974
            2.1.10  Proper substitution of classes for sets into classes   csb 3069
            2.1.11  Define basic set operations and relations   cdif 3138
            2.1.12  Subclasses and subsets   df-ss 3154
            2.1.13  The difference, union, and intersection of two classes   dfdif3 3257
                  2.1.13.1  The difference of two classes   dfdif3 3257
                  2.1.13.2  The union of two classes   elun 3288
                  2.1.13.3  The intersection of two classes   elin 3330
                  2.1.13.4  Combinations of difference, union, and intersection of two classes   unabs 3378
                  2.1.13.5  Class abstractions with difference, union, and intersection of two classes   symdifxor 3413
                  2.1.13.6  Restricted uniqueness with difference, union, and intersection   reuss2 3427
            2.1.14  The empty set   c0 3434
            2.1.15  Conditional operator   cif 3546
            2.1.16  Power classes   cpw 3587
            2.1.17  Unordered and ordered pairs   csn 3604
            2.1.18  The union of a class   cuni 3821
            2.1.19  The intersection of a class   cint 3856
            2.1.20  Indexed union and intersection   ciun 3898
            2.1.21  Disjointness   wdisj 3992
            2.1.22  Binary relations   wbr 4015
            2.1.23  Ordered-pair class abstractions (class builders)   copab 4075
            2.1.24  Transitive classes   wtr 4113
      ​2.2  IZF Set Theory - add the Axioms of Collection and Separation
            2.2.1  Introduce the Axiom of Collection   ax-coll 4130
            2.2.2  Introduce the Axiom of Separation   ax-sep 4133
            2.2.3  Derive the Null Set Axiom   zfnuleu 4139
            2.2.4  Theorems requiring subset and intersection existence   nalset 4145
            2.2.5  Theorems requiring empty set existence   class2seteq 4175
            2.2.6  Collection principle   bnd 4184
      ​2.3  IZF Set Theory - add the Axioms of Power Sets and Pairing
            2.3.1  Introduce the Axiom of Power Sets   ax-pow 4186
            2.3.2  A notation for excluded middle   wem 4206
            2.3.3  Axiom of Pairing   ax-pr 4221
            2.3.4  Ordered pair theorem   opm 4246
            2.3.5  Ordered-pair class abstractions (cont.)   opabid 4269
            2.3.6  Power class of union and intersection   pwin 4294
            2.3.7  Epsilon and identity relations   cep 4299
            ​*2.3.8  Partial and total orderings   wpo 4306
            2.3.9  Founded and set-like relations   wfrfor 4339
            2.3.10  Ordinals   word 4374
      ​2.4  IZF Set Theory - add the Axiom of Union
            2.4.1  Introduce the Axiom of Union   ax-un 4445
            2.4.2  Ordinals (continued)   ordon 4497
      ​2.5  IZF Set Theory - add the Axiom of Set Induction
            2.5.1  The ZF Axiom of Foundation would imply Excluded Middle   regexmidlemm 4543
            2.5.2  Introduce the Axiom of Set Induction   ax-setind 4548
            2.5.3  Transfinite induction   tfi 4593
      ​2.6  IZF Set Theory - add the Axiom of Infinity
            2.6.1  Introduce the Axiom of Infinity   ax-iinf 4599
            2.6.2  The natural numbers   com 4601
            2.6.3  Peano's postulates   peano1 4605
            2.6.4  Finite induction (for finite ordinals)   find 4610
            2.6.5  The Natural Numbers (continued)   nn0suc 4615
            2.6.6  Relations   cxp 4636
            2.6.7  Definite description binder (inverted iota)   cio 5188
            2.6.8  Functions   wfun 5222
            2.6.9  Cantor's Theorem   canth 5842
            2.6.10  Restricted iota (description binder)   crio 5843
            2.6.11  Operations   co 5888
            2.6.12  Maps-to notation   elmpocl 6082
            2.6.13  Function operation   cof 6094
            2.6.14  Functions (continued)   resfunexgALT 6122
            2.6.15  First and second members of an ordered pair   c1st 6152
            ​*2.6.16  Special maps-to operations   opeliunxp2f 6252
            2.6.17  Function transposition   ctpos 6258
            2.6.18  Undefined values   pwuninel2 6296
            2.6.19  Functions on ordinals; strictly monotone ordinal functions   iunon 6298
            2.6.20  "Strong" transfinite recursion   crecs 6318
            2.6.21  Recursive definition generator   crdg 6383
            2.6.22  Finite recursion   cfrec 6404
            2.6.23  Ordinal arithmetic   c1o 6423
            2.6.24  Natural number arithmetic   nna0 6488
            2.6.25  Equivalence relations and classes   wer 6545
            2.6.26  The mapping operation   cmap 6661
            2.6.27  Infinite Cartesian products   cixp 6711
            2.6.28  Equinumerosity   cen 6751
            2.6.29  Equinumerosity (cont.)   xpf1o 6857
            2.6.30  Pigeonhole Principle   phplem1 6865
            2.6.31  Finite sets   fict 6881
            2.6.32  Schroeder-Bernstein Theorem   sbthlem1 6969
            2.6.33  Finite intersections   cfi 6980
            2.6.34  Supremum and infimum   csup 6994
            2.6.35  Ordinal isomorphism   ordiso2 7047
            2.6.36  Disjoint union   cdju 7049
                  2.6.36.1  Disjoint union   cdju 7049
                  ​*2.6.36.2  Left and right injections of a disjoint union   cinl 7057
                  2.6.36.3  Universal property of the disjoint union   djuss 7082
                  2.6.36.4  Dominance and equinumerosity properties of disjoint union   djudom 7105
                  2.6.36.5  Older definition temporarily kept for comparison, to be deleted   cdjud 7114
                  2.6.36.6  Countable sets   0ct 7119
            ​*2.6.37  The one-point compactification of the natural numbers   xnninf 7131
            2.6.38  Omniscient sets   comni 7145
            2.6.39  Markov's principle   cmarkov 7162
            2.6.40  Weakly omniscient sets   cwomni 7174
            2.6.41  Cardinal numbers   ccrd 7191
            2.6.42  Axiom of Choice equivalents   wac 7217
            2.6.43  Cardinal number arithmetic   endjudisj 7222
            2.6.44  Ordinal trichotomy   exmidontriimlem1 7233
            2.6.45  Excluded middle and the power set of a singleton   pw1on 7238
            2.6.46  Apartness relations   wap 7259
​​*PART 3  CHOICE PRINCIPLES
      ​3.1  Countable Choice and Dependent Choice
            3.1.1  Introduce Countable Choice   wacc 7274
​​*PART 4  REAL AND COMPLEX NUMBERS
      ​4.1  Construction and axiomatization of real and complex numbers
            4.1.1  Dedekind-cut construction of real and complex numbers   cnpi 7284
            4.1.2  Final derivation of real and complex number postulates   axcnex 7871
            4.1.3  Real and complex number postulates restated as axioms   ax-cnex 7915
      ​4.2  Derive the basic properties from the field axioms
            4.2.1  Some deductions from the field axioms for complex numbers   cnex 7948
            4.2.2  Infinity and the extended real number system   cpnf 8002
            4.2.3  Restate the ordering postulates with extended real "less than"   axltirr 8037
            4.2.4  Ordering on reals   lttr 8044
            4.2.5  Initial properties of the complex numbers   mul12 8099
      ​4.3  Real and complex numbers - basic operations
            4.3.1  Addition   add12 8128
            4.3.2  Subtraction   cmin 8141
            4.3.3  Multiplication   kcnktkm1cn 8353
            4.3.4  Ordering on reals (cont.)   ltadd2 8389
            4.3.5  Real Apartness   creap 8544
            4.3.6  Complex Apartness   cap 8551
            4.3.7  Reciprocals   recextlem1 8621
            4.3.8  Division   cdiv 8642
            4.3.9  Ordering on reals (cont.)   ltp1 8814
            4.3.10  Suprema   lbreu 8915
            4.3.11  Imaginary and complex number properties   crap0 8928
      ​4.4  Integer sets
            4.4.1  Positive integers (as a subset of complex numbers)   cn 8932
            4.4.2  Principle of mathematical induction   nnind 8948
            ​*4.4.3  Decimal representation of numbers   c2 8983
            ​*4.4.4  Some properties of specific numbers   neg1cn 9037
            4.4.5  Simple number properties   halfcl 9158
            4.4.6  The Archimedean property   arch 9186
            4.4.7  Nonnegative integers (as a subset of complex numbers)   cn0 9189
            ​*4.4.8  Extended nonnegative integers   cxnn0 9252
            4.4.9  Integers (as a subset of complex numbers)   cz 9266
            4.4.10  Decimal arithmetic   cdc 9397
            4.4.11  Upper sets of integers   cuz 9541
            4.4.12  Rational numbers (as a subset of complex numbers)   cq 9632
            4.4.13  Complex numbers as pairs of reals   cnref1o 9663
      ​4.5  Order sets
            4.5.1  Positive reals (as a subset of complex numbers)   crp 9666
            4.5.2  Infinity and the extended real number system (cont.)   cxne 9782
            4.5.3  Real number intervals   cioo 9901
            4.5.4  Finite intervals of integers   cfz 10021
            ​*4.5.5  Finite intervals of nonnegative integers   elfz2nn0 10125
            4.5.6  Half-open integer ranges   cfzo 10155
            4.5.7  Rational numbers (cont.)   qtri3or 10256
      ​4.6  Elementary integer functions
            4.6.1  The floor and ceiling functions   cfl 10281
            4.6.2  The modulo (remainder) operation   cmo 10335
            4.6.3  Miscellaneous theorems about integers   frec2uz0d 10412
            4.6.4  Strong induction over upper sets of integers   uzsinds 10455
            4.6.5  The infinite sequence builder "seq"   cseq 10458
            4.6.6  Integer powers   cexp 10532
            4.6.7  Ordered pair theorem for nonnegative integers   nn0le2msqd 10712
            4.6.8  Factorial function   cfa 10718
            4.6.9  The binomial coefficient operation   cbc 10740
            4.6.10  The ` # ` (set size) function   chash 10768
      ​4.7  Elementary real and complex functions
            4.7.1  The "shift" operation   cshi 10836
            4.7.2  Real and imaginary parts; conjugate   ccj 10861
            4.7.3  Sequence convergence   caucvgrelemrec 11001
            4.7.4  Square root; absolute value   csqrt 11018
            4.7.5  The maximum of two real numbers   maxcom 11225
            4.7.6  The minimum of two real numbers   mincom 11250
            4.7.7  The maximum of two extended reals   xrmaxleim 11265
            4.7.8  The minimum of two extended reals   xrnegiso 11283
      ​4.8  Elementary limits and convergence
            4.8.1  Limits   cli 11299
            4.8.2  Finite and infinite sums   csu 11374
            4.8.3  The binomial theorem   binomlem 11504
            4.8.4  Infinite sums (cont.)   isumshft 11511
            4.8.5  Miscellaneous converging and diverging sequences   divcnv 11518
            4.8.6  Arithmetic series   arisum 11519
            4.8.7  Geometric series   expcnvap0 11523
            4.8.8  Ratio test for infinite series convergence   cvgratnnlembern 11544
            4.8.9  Mertens' theorem   mertenslemub 11555
            4.8.10  Finite and infinite products   prodf 11559
                  4.8.10.1  Product sequences   prodf 11559
                  4.8.10.2  Non-trivial convergence   ntrivcvgap 11569
                  4.8.10.3  Complex products   cprod 11571
                  4.8.10.4  Finite products   fprodseq 11604
      ​4.9  Elementary trigonometry
            4.9.1  The exponential, sine, and cosine functions   ce 11663
                  4.9.1.1  The circle constant (tau = 2 pi)   ctau 11795
            4.9.2  _e is irrational   eirraplem 11797
​​*PART 5  ELEMENTARY NUMBER THEORY
      ​5.1  Elementary properties of divisibility
            5.1.1  The divides relation   cdvds 11807
            ​*5.1.2  Even and odd numbers   evenelz 11885
            5.1.3  The division algorithm   divalglemnn 11936
            5.1.4  The greatest common divisor operator   cgcd 11956
            5.1.5  Bézout's identity   bezoutlemnewy 12010
            5.1.6  Decidable sets of integers   nnmindc 12048
            5.1.7  Algorithms   nn0seqcvgd 12054
            5.1.8  Euclid's Algorithm   eucalgval2 12066
            ​*5.1.9  The least common multiple   clcm 12073
            ​*5.1.10  Coprimality and Euclid's lemma   coprmgcdb 12101
            5.1.11  Cancellability of congruences   congr 12113
      ​5.2  Elementary prime number theory
            ​*5.2.1  Elementary properties   cprime 12120
            ​*5.2.2  Coprimality and Euclid's lemma (cont.)   coprm 12157
            5.2.3  Non-rationality of square root of 2   sqrt2irrlem 12174
            5.2.4  Properties of the canonical representation of a rational   cnumer 12194
            5.2.5  Euler's theorem   codz 12221
            5.2.6  Arithmetic modulo a prime number   modprm1div 12260
            5.2.7  Pythagorean Triples   coprimeprodsq 12270
            5.2.8  The prime count function   cpc 12297
            5.2.9  Pocklington's theorem   prmpwdvds 12366
            5.2.10  Infinite primes theorem   infpnlem1 12370
            5.2.11  Fundamental theorem of arithmetic   1arithlem1 12374
            5.2.12  Lagrange's four-square theorem   cgz 12380
      ​5.3  Cardinality of real and complex number subsets
            5.3.1  Countability of integers and rationals   oddennn 12406
​PART 6  BASIC STRUCTURES
      ​6.1  Extensible structures
            ​*6.1.1  Basic definitions   cstr 12471
            6.1.2  Slot definitions   cplusg 12550
            6.1.3  Definition of the structure product   crest 12705
            6.1.4  Definition of the structure quotient   cimas 12737
​PART 7  BASIC ALGEBRAIC STRUCTURES
      ​7.1  Monoids
            ​*7.1.1  Magmas   cplusf 12790
            ​*7.1.2  Identity elements   mgmidmo 12809
            ​*7.1.3  Semigroups   csgrp 12825
            ​*7.1.4  Definition and basic properties of monoids   cmnd 12838
            7.1.5  Monoid homomorphisms and submonoids   cmhm 12870
      ​7.2  Groups
            7.2.1  Definition and basic properties   cgrp 12898
            ​*7.2.2  Group multiple operation   cmg 13013
            7.2.3  Subgroups and Quotient groups   csubg 13058
            7.2.4  Abelian groups   ccmn 13120
                  7.2.4.1  Definition and basic properties   ccmn 13120
      ​7.3  Rings
            7.3.1  Multiplicative Group   cmgp 13170
            ​*7.3.2  Non-unital rings ("rngs")   crng 13182
            ​*7.3.3  Ring unity (multiplicative identity)   cur 13206
            7.3.4  Semirings   csrg 13210
            7.3.5  Definition and basic properties of unital rings   crg 13243
            7.3.6  Opposite ring   coppr 13310
            7.3.7  Divisibility   cdsr 13329
            7.3.8  Ring homomorphisms   crh 13393
            7.3.9  Nonzero rings and zero rings   cnzr 13397
            7.3.10  Local rings   clring 13405
            7.3.11  Subrings   csubrng 13412
                  7.3.11.1  Subrings of non-unital rings   csubrng 13412
                  7.3.11.2  Subrings of unital rings   csubrg 13432
      ​7.4  Division rings and fields
            7.4.1  Ring apartness   capr 13464
      ​7.5  Left modules
            7.5.1  Definition and basic properties   clmod 13471
            7.5.2  Subspaces and spans in a left module   clss 13536
      ​7.6  Subring algebras and ideals
            7.6.1  Subring algebras   csra 13617
            7.6.2  Ideals and spans   clidl 13651
            7.6.3  Two-sided ideals and quotient rings   c2idl 13679
      ​7.7  The complex numbers as an algebraic extensible structure
            7.7.1  Definition and basic properties   cpsmet 13696
            ​*7.7.2  Ring of integers   czring 13737
            7.7.3  Algebraic constructions based on the complex numbers   czrh 13754
​PART 8  BASIC TOPOLOGY
      ​8.1  Topology
            ​*8.1.1  Topological spaces   ctop 13768
                  8.1.1.1  Topologies   ctop 13768
                  8.1.1.2  Topologies on sets   ctopon 13781
                  8.1.1.3  Topological spaces   ctps 13801
            8.1.2  Topological bases   ctb 13813
            8.1.3  Examples of topologies   distop 13856
            8.1.4  Closure and interior   ccld 13863
            8.1.5  Neighborhoods   cnei 13909
            8.1.6  Subspace topologies   restrcl 13938
            8.1.7  Limits and continuity in topological spaces   ccn 13956
            8.1.8  Product topologies   ctx 14023
            8.1.9  Continuous function-builders   cnmptid 14052
            8.1.10  Homeomorphisms   chmeo 14071
      ​8.2  Metric spaces
            8.2.1  Pseudometric spaces   psmetrel 14093
            8.2.2  Basic metric space properties   cxms 14107
            8.2.3  Metric space balls   blfvalps 14156
            8.2.4  Open sets of a metric space   mopnrel 14212
            8.2.5  Continuity in metric spaces   metcnp3 14282
            8.2.6  Topology on the reals   qtopbasss 14292
            8.2.7  Topological definitions using the reals   ccncf 14328
​PART 9  BASIC REAL AND COMPLEX ANALYSIS
            9.0.1  Dedekind cuts   dedekindeulemuub 14366
            9.0.2  Intermediate value theorem   ivthinclemlm 14383
      ​9.1  Derivatives
            9.1.1  Real and complex differentiation   climc 14394
                  9.1.1.1  Derivatives of functions of one complex or real variable   climc 14394
​PART 10  BASIC REAL AND COMPLEX FUNCTIONS
      ​10.1  Basic trigonometry
            10.1.1  The exponential, sine, and cosine functions (cont.)   efcn 14460
            10.1.2  Properties of pi = 3.14159...   pilem1 14471
            10.1.3  The natural logarithm on complex numbers   clog 14548
            ​*10.1.4  Logarithms to an arbitrary base   clogb 14632
            10.1.5  Quartic binomial expansion   binom4 14668
      ​10.2  Basic number theory
            ​*10.2.1  Quadratic residues and the Legendre symbol   clgs 14669
            10.2.2  Quadratic reciprocity   lgseisenlem1 14721
            10.2.3  All primes 4n+1 are the sum of two squares   2sqlem1 14732
​PART 11  GUIDES AND MISCELLANEA
      ​11.1  Guides (conventions, explanations, and examples)
            ​*11.1.1  Conventions   conventions 14744
            11.1.2  Definitional examples   ex-or 14745
​PART 12  SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
      ​12.1  Mathboxes for user contributions
            12.1.1  Mathbox guidelines   mathbox 14755
      ​12.2  Mathbox for BJ
            12.2.1  Propositional calculus   bj-nnsn 14756
                  ​*12.2.1.1  Stable formulas   bj-trst 14762
                  12.2.1.2  Decidable formulas   bj-trdc 14775
            12.2.2  Predicate calculus   bj-ex 14785
            12.2.3  Set theorey miscellaneous   bj-el2oss1o 14797
            ​*12.2.4  Extensionality   bj-vtoclgft 14798
            ​*12.2.5  Decidability of classes   wdcin 14816
            12.2.6  Disjoint union   djucllem 14823
            12.2.7  Miscellaneous   funmptd 14826
            ​*12.2.8  Constructive Zermelo--Fraenkel set theory (CZF): Bounded formulas and classes   wbd 14835
                  *12.2.8.1  Bounded formulas   wbd 14835
                  ​*12.2.8.2  Bounded classes   wbdc 14863
            ​*12.2.9  CZF: Bounded separation   ax-bdsep 14907
                  12.2.9.1  Delta_0-classical logic   ax-bj-d0cl 14947
                  12.2.9.2  Inductive classes and the class of natural number ordinals   wind 14949
                  ​*12.2.9.3  The first three Peano postulates   bj-peano2 14962
            ​*12.2.10  CZF: Infinity   ax-infvn 14964
                  *12.2.10.1  The set of natural number ordinals   ax-infvn 14964
                  ​*12.2.10.2  Peano's fifth postulate   bdpeano5 14966
                  ​*12.2.10.3  Bounded induction and Peano's fourth postulate   findset 14968
            ​*12.2.11  CZF: Set induction   setindft 14988
                  *12.2.11.1  Set induction   setindft 14988
                  ​*12.2.11.2  Full induction   bj-findis 15002
            ​*12.2.12  CZF: Strong collection   ax-strcoll 15005
            ​*12.2.13  CZF: Subset collection   ax-sscoll 15010
            12.2.14  Real numbers   ax-ddkcomp 15012
      ​12.3  Mathbox for Jim Kingdon
            12.3.1  Propositional and predicate logic   nnnotnotr 15013
            12.3.2  Natural numbers   1dom1el 15014
            12.3.3  The power set of a singleton   pwtrufal 15019
            12.3.4  Omniscience of NN+oo   0nninf 15025
            12.3.5  Schroeder-Bernstein Theorem   exmidsbthrlem 15042
            12.3.6  Real and complex numbers   qdencn 15047
            ​*12.3.7  Analytic omniscience principles   trilpolemclim 15056
            12.3.8  Supremum and infimum   supfz 15091
            12.3.9  Circle constant   taupi 15093
      ​12.4  Mathbox for Mykola Mostovenko
      ​12.5  Mathbox for David A. Wheeler
            12.5.1  Testable propositions   dftest 15095
            ​*12.5.2  Allsome quantifier   walsi 15096