Project-declaredLean 4.32.1 · mathlib@520045ab

Step Vec of Fn

LO.FirstOrder.Semiterm.stepVec_ofFn

formal logic metatheory proof theory primrec coding

Plain-language statement

With every lookup present and non-zero, the fold rebuilds the vecToNat code of the arguments.

Exact Lean statement

lemma stepVec_ofFn {T : List ℕ} {a : ℕ} {w u : Fin a → ℕ}
    (h : ∀ i, T.getD (w i) 0 = u i + 1) :
    stepVec T (List.ofFn w) = Matrix.vecToNat u + 1

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

lemma stepVec_ofFn {T : List ℕ} {a : ℕ} {w u : Fin a → ℕ}    (h : ∀ i, T.getD (w i) 0 = u i + 1) :    stepVec T (List.ofFn w) = Matrix.vecToNat u + 1 := by  induction a with  | zero => simp [Matrix.vecToNat]  | succ a ih =>    rw [List.ofFn_succ, stepVec_cons,      ih (w := fun i ↦ w i.succ) (u := fun i ↦ u i.succ) fun i ↦ by simpa using h i.succ,      h 0, if_neg (by simp)]    simp only [Nat.add_sub_cancel]    simpa using (Matrix.encode_succ (u 0) (fun i ↦ u i.succ)).symm

Project: Foundation
License: Apache-2.0
Commit: 8dcdb3196454
Source: Foundation/FirstOrder/Basic/PrimrecCoding.lean:168-178

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Source project: Foundation

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