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Proof step 8 from proof append-to-gr-01 (previous step)

1 + # x0 < m, ∀ m, σ. # x0 < m → ⌜x0⌝ + σ to m = ⌜x0⌝ + (σ to (m - # x0)) ⊦ ⌜x0⌝ + σ to (m - 1) = ⌜x0⌝ + (σ to (m - 1 + # x0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
m = m0 + 1, 1 + # x0 < m, ∀ m, σ. # x0 < m → ⌜x0⌝ + σ to m = ⌜x0⌝ + (σ to (m - # x0)) ⊦ m = 0, ⌜x0⌝ + σ to m0 = ⌜x0⌝ + (σ to (m - 1 + # x0))

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m, m1]

Additional information

Used simplifier rules: n0 < n ⊦ ¬ m + (* n) < (* n0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m, m1