Theorems · Theorem
Function.eq_update_iff
∀ {α : Sort u} {β : α → Sort v} [inst : DecidableEq α] {a : α} {b : β a} {f g : (a : α) → β a},
g = Function.update f a b ↔ g a = b ∧ ∀ (x : α), x ≠ a → g x = f x- Defined in
- Mathlib.Logic.Function.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.updatestatement · cited by 502
- Function.forall_update_iffproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- Function.update_comp_eq_of_injective'proof · cited by 3
- nhds_nhdsAdjointproof · cited by 2
- dslope_sub_smulproof · cited by 1