ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-case GIF version

Definition df-case 7283
Description: The "case" construction: if 𝐹:𝐴𝑋 and 𝐺:𝐵𝑋 are functions, then case(𝐹, 𝐺):(𝐴𝐵)⟶𝑋 is the natural function obtained by a definition by cases, hence the name. It is the unique function whose existence is asserted by the universal property of disjoint unions updjud 7281. The definition is adapted to make sense also for binary relations (where the universal property also holds). (Contributed by MC and BJ, 10-Jul-2022.)
Assertion
Ref Expression
df-case case(𝑅, 𝑆) = ((𝑅inl) ∪ (𝑆inr))

Detailed syntax breakdown of Definition df-case
StepHypRef Expression
1 cR . . 3 class 𝑅
2 cS . . 3 class 𝑆
31, 2cdjucase 7282 . 2 class case(𝑅, 𝑆)
4 cinl 7244 . . . . 5 class inl
54ccnv 4724 . . . 4 class inl
61, 5ccom 4729 . . 3 class (𝑅inl)
7 cinr 7245 . . . . 5 class inr
87ccnv 4724 . . . 4 class inr
92, 8ccom 4729 . . 3 class (𝑆inr)
106, 9cun 3198 . 2 class ((𝑅inl) ∪ (𝑆inr))
113, 10wceq 1397 1 wff case(𝑅, 𝑆) = ((𝑅inl) ∪ (𝑆inr))
Colors of variables: wff set class
This definition is referenced by:  casefun  7284  casedm  7285  caserel  7286  caseinj  7288  caseinl  7290  caseinr  7291
  Copyright terms: Public domain W3C validator