Theorems · Definition

Equiv.subtypeEquivCodomain

{X : Sort u_9} →
  {Y : Sort u_10} → [DecidableEq X] → {x : X} → (f : { x' // x' ≠ x } → Y) → { g // g ∘ Subtype.val = f } ≃ Y

The type of all functions X → Y with prescribed values for all x' ≠ x is equivalent to the codomain Y.

Defined in: Mathlib.Logic.Equiv.Basic
Cited by: 7 results in Mathlib
Foundations: Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DecidableEq

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