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Proof step 4 from proof get-from-01 (previous step)

m + m0 ≤ # x0, ∀ m, m0. m + m0 < # x0 → (x0 from m)[m0] = x0[m + m0] ∨ x0 = [] ⊦ (a ' + x0 from m)[m0] = (a ' + x0)[m + m0]

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ m0, x0, a. m1 + m0 ≤ # x0 ∧ (∀ m, m0. m + m0 < # x0 → (x0 from m)[m0] = x0[m + m0] ∨ x0 = []) → (a ' + x0 from m1)[m0] = (a ' + x0)[m1 + m0], m1 +1 + m0 ≤ # x0, ∀ m, m0. m + m0 < # x0 → (x0 from m)[m0] = x0[m + m0] ∨ x0 = [] ⊦ (a ' + x0 from m1 +1)[m0] = (a ' + x0)[m1 +1 + m0]

Rule argument

indvar: m

Additional information

Used simplifier rules: from-zero-l: ⊦ x from 0 = x;%nat freely generated by 0, +1;;%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