decidableEqPFun — Mathlib

English

If f is surjective, then for any property p on β there is a y with p(y) equivalent to some x with p(f(x)).

Русский

Если f сюръективна, то свойство p на β эквивалентно свойству p на образах f(x).

LaTeX

$$$\\operatorname{Surjective}(f) \\rightarrow (\\forall p:\\beta\\to\\operatorname{Prop}, (\\exists y\,p(y)) \\iff (\\exists x\, p(f(x))))$$$

Lean4

instance decidableEqPFun (p : Prop) [Decidable p] (α : p → Type*) [∀ hp, DecidableEq (α hp)] : DecidableEq (∀ hp, α hp)
  | f, g => decidable_of_iff (∀ hp, f hp = g hp) funext_iff.symm

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