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Proof step 2 from proof append-from-le-01 (previous step)

m ≤ # x ⊦ ⌜x⌝ + σ from m = ⌜x from m⌝ + σ

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ m, σ. m ≤ # x0 → ⌜x0⌝ + σ from m = ⌜x0 from m⌝ + σ, m ≤ #(a + x0) ⊦ ⌜a + x0⌝ + σ from m = ⌜a + x0 from m⌝ + σ

Rule argument

indvar: x

Additional information

Used simplifier rules: empty: ⊦ ⌜[]⌝ = [];%empty-append: ⊦ [] + σ = σ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%from-zero: ⊦ σ from 0 = σ;%from-zero-l: ⊦ x from 0 = x;%list freely generated by [], +;;%size-01: ⊦ # [] = 0; from specification list-data%lez-01: ⊦ m ≤ 0 ↔ m = 0; from specification nat