TOC of Theorem List - Quantum Logic Explorer

Table of Contents Summary

      0.1  Ortholattices
      0.2  Weakly orthomodular lattices
      0.3  Orthomodular lattices
      0.4  Derivation of 4-variable proper OA from OA distributive law
      0.5  Orthoarguesian laws
      0.6  Other stronger-than-OML laws
      0.7  Contributions of Roy F. Longton
      0.8  Weakly distributive ortholattices (WDOL)
      0.9  Modular ortholattices (MOL)

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

      ​0.1  Ortholattices
            0.1.1  Basic syntax and axioms   wb 1
            0.1.2  Basic lemmas   id 59
            0.1.3  Relationship analogues (ordering; commutation)   df-le 129
            0.1.4  Commutator (ortholattice theorems)   cmtrcom 190
            ​*0.1.5  Weak "orthomodular law" in ortholattices.   wa1 191
            0.1.6  Kalmbach axioms (soundness proofs) that are true in all ortholattices   sklem 230
      ​0.2  Weakly orthomodular lattices
            0.2.1  Weak orthomodular law   ax-wom 361
            0.2.2  Weakly orthomodular lattices   wom3 367
            0.2.3  Relationship analogues (ordering; commutation) in WOML   wleoa 376
            0.2.4  Kalmbach axioms (soundness proofs) that require WOML   ska2 432
            0.2.5  Weak orthomodular law variants   woml6 436
      ​0.3  Orthomodular lattices
            0.3.1  Orthomodular law   ax-r3 439
            0.3.2  Relationship analogues using OML (ordering; commutation)   oml2 451
            0.3.3  Commutator (orthomodular lattice theorems)   cmtr1com 493
            0.3.4  Kalmbach conditional   i3bi 496
            0.3.5  Unified disjunction   ud1lem1 560
            0.3.6  Lemmas for unified implication study   u1lemaa 600
            0.3.7  Some proofs contributed by Josiah Burroughs   u1lemn1b 730
            0.3.8  More lemmas for unified implication   u1lem1 734
            0.3.9  Some 3-variable theorems   3vth1 804
            0.3.10  OML lemmas for studying Godowski equations   govar 896
            0.3.11  OML lemmas for studying orthoarguesian laws   oas 925
            0.3.12  5OA law   oa8todual 971
            0.3.13  "Godowski/Greechie" form of proper 4-OA   oa4to4u 973
            0.3.14  Some 3-OA inferences (derived under OM)   oa3-2lema 978
      ​​*0.4  Derivation of 4-variable proper OA from OA distributive law
      ​​*0.5  Orthoarguesian laws
            0.5.1  3-variable orthoarguesian law   ax-3oa 998
            0.5.2  4-variable orthoarguesian law   ax-oal4 1026
            0.5.3  6-variable orthoarguesian law   ax-oa6 1030
            0.5.4  The proper 4-variable orthoarguesian law   ax-4oa 1033
      ​0.6  Other stronger-than-OML laws
            0.6.1  New state-related equation   ax-newstateeq 1045
      ​0.7  Contributions of Roy F. Longton
            0.7.1  Roy F. Longton's first section   lem3.3.2 1046
            0.7.2  Roy F. Longton's second section   lem3.4.1 1075
            0.7.3  Roy F. Longton's third section   lem4.6.2e1 1082
      ​0.8  Weakly distributive ortholattices (WDOL)
            0.8.1  WDOL law   ax-wdol 1104
      ​0.9  Modular ortholattices (MOL)
            0.9.1  Modular law   ax-ml 1122
            0.9.2  Arguesian law   ax-arg 1153