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Theorems · Theorem · logic and foundations

Nat.Subtype.succ.congr_simp

∀ {s : Set ℕ} [inst : Infinite ↑s] [inst_1 : DecidablePred fun x => x ∈ s] (x x_1 : ↑s),
  x = x_1 → Nat.Subtype.succ x = Nat.Subtype.succ x_1
Defined in
Mathlib.Logic.Denumerable
Cited by
0 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
InfiniteDecidablePred
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemInfinite · cited by 352InfiniteNat.Subtype.succ · cited by 6Subtype.succsucc.congr_simpCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Setstatement and proof · cited by 53,352
  • Set.Elemstatement and proof · cited by 7,166
  • Infinitestatement and proof · cited by 352
  • Nat.Subtype.succstatement and proof · cited by 6

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