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Proof step 7 from proof blastN-mklist (previous step)

n0 = m + 1, ∀ x, a. butlastn(n0, x + mklist(a, n0)) = x ⊦ butlastn(n0, x + a ' + mklist(a, m)) = x, n0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ x0, a0. butlastn(m, (x0 + mklist(a0, m + 1)).butlast) = x0 ⊦ butlastn(m, x + (a ' + mklist(a, m)).butlast) = x

Rule argument

Additional information

Used simplifier rules: butlastN-rec: ⊦ butlastn(n + 1, x) = butlastn(n, x.butlast);%bin: ⊦ (x + a ' + y).butlast = x + (a ' + y).butlast;%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%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