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Theorems · Theorem · logic and foundations

mem_dite

∀ {α : Type u_1} {β : Type u_2} [inst : Membership α β] {p : Prop} [inst_1 : Decidable p] {a : α} {s : p → β}
  {t : ¬p → β}, (a ∈ if h : p then s h else t h) ↔ (∀ (h : p), a ∈ s h) ∧ ∀ (h : ¬p), a ∈ t h
Defined in
Mathlib.Logic.Basic
Cited by
1 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext, Quot.sound
Assumes
MembershipDecidable
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mem_ite · cited by 0mem_itemem_diteCITED BYCITES

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