Theorems · Theorem · logic and foundations
Part.ext
∀ {α : Type u_1} {o p : Part α}, (∀ (a : α), a ∈ o ↔ a ∈ p) → o = pPart extensionality
- Defined in
- Mathlib.Data.Part
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Partstatement and proof · cited by 325
- Part.Domproof · cited by 145
- Part.getproof · cited by 77
- Exists.fstproof · cited by 22
- Exists.sndproof · cited by 13
- Part.ext'proof · cited by 6
Cited by24
Results whose statement or proof uses this declaration.
- Part.bind_someproof · cited by 49
- PFun.extproof · cited by 8
- Part.bind_some_eq_mapproof · cited by 6
- Part.eq_none_iffproof · cited by 6
- Part.bind_assocproof · cited by 5
- StateTransition.reaches_evalproof · cited by 4
- Part.assert_negproof · cited by 2
- Nat.Partrec.Code.eval_eq_rfindOptproof · cited by 2
- Partrec.nat_casesOn_rightproof · cited by 2
- Turing.ToPartrec.cont_eval_fixproof · cited by 2
- Nat.Partrec.prec'proof · cited by 1
- Part.assert_posproof · cited by 1