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Proof step 2 from proof blastN-mklist (previous step)

∀ x, a. butlastn(n0, x + mklist(a, n0)) = x ⊦ butlastn(n0 +1, x + mklist(a, n0 +1)) = x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ x, a. butlastn(n0, x + mklist(a, n0)) = x ⊦ butlastn(n0, x + (a ' + mklist(a, n0)).butlast) = x

Rule argument

Additional information

Used simplifier rules: mk-plus: ⊦ mklist(a, m + n) = mklist(a, m) + mklist(a, n);%mklist-one: ⊦ mklist(a, 1) = a ';%mk-last: ⊦ mklist(a, n) + a ' = a ' + mklist(a, n);%butlastN-rec: ⊦ butlastn(n + 1, x) = butlastn(n, x.butlast);%bin: ⊦ (x + a ' + y).butlast = x + (a ' + y).butlast;%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%a: ⊦ (x + y) + z = x + y + z; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2