Theorems · Theorem · order theory
Nat.leRecOn_succ
∀ {C : ℕ → Sort u_1} {n m : ℕ} (h1 : n ≤ m) {h2 : n ≤ m + 1} {next : {k : ℕ} → C k → C (k + 1)} (x : C n),
Nat.leRecOn h2 next x = next (Nat.leRecOn h1 (fun {k} => next) x)- Defined in
- Mathlib.Data.Nat.Init
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses no axioms
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.
- Nat.leRecOnstatement · cited by 13
- Nat.leRec_succproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- FirstOrder.Language.DirectedSystem.coe_natLERecproof · cited by 0
- Nat.leRecOn_surjectiveproof · cited by 0
- Metric.toInductiveLimit_commuteproof · cited by 0
- Nat.leRecOn_injectiveproof · cited by 0