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Theorems · Theorem · order theory

Nat.leRec_trans

∀ {n m k : ℕ} {motive : (m : ℕ) → n ≤ m → Sort u_1} (refl : motive n ⋯)
  (le_succ_of_le : ⦃k : ℕ⦄ → (h : n ≤ k) → motive k h → motive (k + 1) ⋯) (hnm : n ≤ m) (hmk : m ≤ k),
  Nat.leRec refl le_succ_of_le ⋯ =
    Nat.leRec (Nat.leRec refl (fun x h => le_succ_of_le h) hnm) (fun x h => le_succ_of_le ⋯) hmk
Defined in
Mathlib.Data.Nat.Init
Cited by
2 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Nat.leRec_succ_left · cited by 1Nat.leRec_succ_leftNat.leRecOn_trans · cited by 0Nat.leRecOn_transNat.leRec · cited by 13Nat.leRecNat.leRec_self · cited by 7Nat.leRec_selfNat.leRec_succ · cited by 6Nat.leRec_succNat.leRec_transCITED BYCITES

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Cited by2

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