Theorems · Theorem · logic and foundations
Part.fix_def
∀ {α : Type u_1} {β : α → Type u_2} (f : ((a : α) → Part (β a)) → (a : α) → Part (β a)) {x : α}
(h' : ∃ i, (Part.Fix.approx f i x).Dom), Part.fix f x = Part.Fix.approx f (Nat.find h').succ x- Defined in
- Mathlib.Control.Fix
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.Domstatement and proof · cited by 145
- Nat.findstatement and proof · cited by 139
- Nat.find_specproof · cited by 74
- Part.noneproof · cited by 36
- Nat.find_minproof · cited by 30
- Part.Fix.approxstatement and proof · cited by 11
- Part.assertproof · cited by 10
- Part.fixstatement · cited by 9
- Nat.Uptoproof · cited by 2
- Part.assert_negproof · cited by 2
- Nat.Upto.succproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Part.Fix.mem_iffproof · cited by 2