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Theorems · Theorem · logic and foundations

ite_mem

∀ {α : Type u_1} {β : Type u_2} [inst : Membership α β] {p : Prop} [inst_1 : Decidable p] {a b : α} {s : β},
  (if p then a else b) ∈ s ↔ (p → a ∈ s) ∧ (¬p → b ∈ s)
Defined in
Mathlib.Logic.Basic
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
Assumes
MembershipDecidable
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.diagonal_mem_matrix_iff · cited by 0Matrix.diagonal_mem_matri…Matrix.single_mem_matrix · cited by 0Matrix.single_mem_matrixdite_mem · cited by 1dite_memite_memCITED BYCITES

Cites1

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.