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Proof step 4 from proof append-from-le-01 (previous step)

m ≤ # x0 + 1, ∀ m, σ. m ≤ # x0 → ⌜x0⌝ + σ from m = ⌜x0 from m⌝ + σ ⊦ (⌜a '⌝ + ⌜x0⌝ ) + σ from m = ⌜a ' + x0 from m⌝ + σ

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ x0, a, σ. m0 ≤ # x0 + 1 ∧ (∀ m, σ. m ≤ # x0 → ⌜x0⌝ + σ from m = ⌜x0 from m⌝ + σ) → (⌜a '⌝ + ⌜x0⌝ ) + σ from m0 = ⌜a ' + x0 from m0⌝ + σ, m0 +1 ≤ # x0 + 1, ∀ m, σ. m ≤ # x0 → ⌜x0⌝ + σ from m = ⌜x0 from m⌝ + σ ⊦ (⌜a '⌝ + ⌜x0⌝ ) + σ from m0 +1 = ⌜a ' + x0 from m0 +1⌝ + σ

Rule argument

indvar: m

Additional information

Used simplifier rules: from-zero: ⊦ σ from 0 = σ;%from-zero-l: ⊦ x from 0 = x;%append-finfin: ⊦ ⌜x + y⌝ = ⌜x⌝ + ⌜y⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%append-cancel-l: ⊦ ⌜x⌝ + σ0 = ⌜x⌝ + σ1 ↔ σ0 = σ1;%nat freely generated by 0, +1;;%a: ⊦ (x + y) + z = x + y + z; from specification list