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Proof step 29 from proof from-append-add (previous step)

nf0(n0 + n1 + n) = ((σ to n) + ⌜nf⌝ )[n0 + n1 + n] ⊦ ((σ to n) + ⌜nf⌝ )[n0 + n1 + n] = nf(n0 + n1), # σ < ⌜n⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: get-append-notls seq: ⊦ ¬ ⌜m⌝ < # σ → (σ + σ1)[m] = σ1[m - (# σ).n] subst: [m, σ1, σ] → [n0 + n1 + n, ⌜nf⌝ , σ to n] flags: rewrite, current

Additional information

Used simplifier rules: get-append-ls: ⊦ ⌜m⌝ < # σ → (σ + σ1)[m] = σ[m];%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%size-to: ¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝ ;%size-to: ¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝ ;%sel-inf: ⊦ ⌜nf⌝ [n] = nf(n);%sel: ⊦ ⌜m⌝ .n = m; from specification nat-inf-basic%eq-01: ⊦ m + n - m = n; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%add-fin: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; from specification nat-inf%ls-natinf-to-nat-3-1: ⊦ ⌜n1⌝ + ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ ↔ n1 + n + m < n0; from specification nat-inf%l-02: ⊦ ¬ m + n < m; from specification nat-basic2%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf Used terms: n0 + n1 + n, ⌜nf⌝ , σ to n