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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: append-finfin: ⊦ ⌜x + y⌝ = ⌜x⌝ + ⌜y⌝ ;% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)