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Proof step 2 from proof get-last2 (previous step)

∀ a. (a ' + x0)[# x0] = (a ' + x0).last ⊦ (a ' + (a0 + x0))[#(a0 + x0)] = (a ' + (a0 + x0)).last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ a. (a ' + x0)[# x0] = (a ' + x0).last ⊦ (a0 ' + x0)[# x0] = (a0 ' + x0).last

Rule argument

Additional information

Used simplifier rules: get-succ: ⊦ (a ' + x)[n + 1] = x[n];%l-05: ⊦ (b ' + a ' + x).last = (a ' + x).last; from specification list-last%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%succ: ⊦ m +1 = m + 1; from specification nat-basic2%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list