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

m ≤ # x ⊦ ⌜x⌝ + σ to m = ⌜x to m⌝

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: x

Additional information

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