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Theorems · Theorem · order theory

dite_ne_bot

∀ {α : Type u} [inst : Bot α] {p : Prop} [inst_1 : Decidable p] {a : p → α} {b : ¬p → α},
  (∀ (h : p), a h ≠ ⊥) → (∀ (h : ¬p), b h ≠ ⊥) → (if h : p then a h else b h) ≠ ⊥
Defined in
Mathlib.Order.BoundedOrder.Basic
Cited by
1 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
BotDecidable
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ite_ne_bot · cited by 0ite_ne_botBot.bot · cited by 4720Bot.botBot · cited by 96Botdite_ne_botCITED BYCITES

Cites2

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  • Bot.botstatement and proof · cited by 4,720
  • Botstatement and proof · cited by 96

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