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Proof step 7 from proof append-to-gr-01 (previous step)

1 + # x0 < m, ∀ m, σ. # x0 < m → ⌜x0⌝ + σ to m = ⌜x0⌝ + (σ to (m - # x0)) ⊦ ⌜a '⌝ + (⌜x0⌝ + σ to (m - 1)) = (⌜a '⌝ + ⌜x0⌝ ) + (σ to (m - 1 + # x0)), m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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))

Rule argument

Additional information

Used simplifier rules: append-cancel-l: ⊦ ⌜x⌝ + σ0 = ⌜x⌝ + σ1 ↔ σ0 = σ1;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;% ⊦ m < n → n ≠ 0; (s)