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Proof step 9 from proof blastN-mklist (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: mk-last-02 seq: ⊦ n ≠ 0 → mklist(a, n) = mklist(a, n -1) + a ' subst: [n, a] → [m + 1, a] flags: <all paths>

Additional information

Used simplifier rules: mk-last: ⊦ mklist(a, n) + a ' = a ' + mklist(a, n);%bin: ⊦ (x + a ' + y).butlast = x + (a ' + y).butlast;% ⊦ (m + 1)-1 = m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ m + 1 ≠ 0; (s) Used terms: m + 1, a