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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ σ, m. ⌜x0⌝ + σ from m + # x0 = σ from m ⊦ ⌜x0⌝ + σ from m + # x0 = σ from m

Rule argument

Additional information

Used simplifier rules: append-finfin: ⊦ ⌜x + y⌝ = ⌜x⌝ + ⌜y⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%from-succ-cons: ⊦ ⌜a '⌝ + σ from n + 1 = σ from n;%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)