Mathlib Map

Theorems · Theorem · order theory

ite_ne_bot

∀ {α : Type u} [inst : Bot α] {p : Prop} [inst_1 : Decidable p] {a b : α},
  (p → a ≠ ⊥) → (¬p → b ≠ ⊥) → (if p then a else b) ≠ ⊥
Defined in
Mathlib.Order.BoundedOrder.Basic
Cited by
0 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
BotDecidable

Around this declaration

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

Cites3

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

  • Bot.botstatement and proof · cited by 4,720
  • Botstatement and proof · cited by 96
  • dite_ne_botproof · cited by 1

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.