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Proof step 1 from proof append-from-addsize-01 (conclusion)

⊦ ⌜x⌝ + σ from m + # x = σ from m

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ σ, m. ⌜x0⌝ + σ from m + # x0 = σ from m ⊦ ⌜a + x0⌝ + σ from m + #(a + x0) = σ from m

Rule argument

indvar: x

Additional information

Used simplifier rules: empty: ⊦ ⌜[]⌝ = [];%empty-append: ⊦ [] + σ = σ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%list freely generated by [], +;;%size-01: ⊦ # [] = 0; from specification list-data%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2