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Proof step 17 from proof prepost-encode-group-nodes (previous step)

# buf1 = gndx1.flashsize, # buf0 = gndx0.flashsize, # gndx0 = # lax, gndx1.flashsize < 2 * NODE_HEADER_SIZE + (gndx0 + gndx1)[# lax].alignedsize, abs-nodes(buf0, n, gndx0, lax, false) ⊦ # lax + # gndx1 = 0, gndx1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del, inst: group-store name: get-append-grt seq: ⊦ ¬ n < # gndx → (gndx + gndx0)[n] = gndx0[n - # gndx] subst: [n, gndx0, gndx] → [# lax, gndx1, gndx0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n < # gndx → (gndx + gndx0)[n] = gndx[n]; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ 2 * NODE_HEADER_SIZE + n ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # lax = 0 ↔ lax = []; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: # lax, gndx1, gndx0