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Proof step 12 from proof append-to-gr-01 (previous step)

∀ m, σ. # x0 < m → ⌜x0⌝ + σ to m = ⌜x0⌝ + (σ to (m - # x0)) ⊦ n0 = 0, ⌜x0⌝ + σ to n0 + # x0 = ⌜x0⌝ + (σ to n0)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 1 terms: n0 + # x0, σ

Additional information

Used simplifier rules: ⊦ m < m + n ↔ n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n - m = n; (s) Used terms: n0 + # x0, σ