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Proof step 4 from proof append-to-gr-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ n ≠ 0 → ⌜a '⌝ + σ to (* n) = ⌜a '⌝ + (σ to (n - 1))
Proof step 6:
m ≠ 0, # x0 + 1 < m, ∀ m, σ. # x0 < m → ⌜x0⌝ + σ to m = ⌜x0⌝ + (σ to (m - # x0)) ∨ m = 0 ⊦ m = 0, ⌜a '⌝ + (⌜x0⌝ + σ to (m - 1)) = (⌜a '⌝ + ⌜x0⌝ ) + (σ to (m - # x0 + 1))

Rule argument

spec: stream inst: name: cons-to-num seq: ⊦ n ≠ 0 → ⌜a '⌝ + σ to (* n) = ⌜a '⌝ + (σ to (n - 1)) subst: [n, σ, a] → [m, ⌜x0⌝ + σ, a] flags: rewrite, current

Additional information

Used simplifier rules: append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2; Used terms: m, ⌜x0⌝ + σ, a