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Proof step 5 from proof contractinf-tl (previous step)

⊦ (⌜nf(0) '⌝ + ⌜λ n. nf(n + 1)⌝ )[n] = nf(n)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ⌜m⌝ < # σ → (σ + σ1)[m] = σ[m]
Proof step 7:
¬ ⌜n⌝ < # ⌜nf(0) '⌝ ⊦ (⌜nf(0) '⌝ + ⌜λ n. nf(n + 1)⌝ )[n] = nf(n)

Rule argument

spec: inst: name: get-append-ls seq: ⊦ ⌜m⌝ < # σ → (σ + σ1)[m] = σ[m] subst: [m, σ1, σ] → [n, ⌜λ n. nf(n + 1)⌝ , ⌜nf(0) '⌝ ] flags: rewrite, current

Additional information

Used simplifier rules: sel-fin: ⊦ ⌜x⌝ [n] = x[n];%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%len-02: ⊦ # a ' = 0 +1; from specification list%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%one-03: ⊦ a '[0] = a; from specification list-del Used terms: n, ⌜λ n. nf(n + 1)⌝ , ⌜nf(0) '⌝