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

m ≤ n0 + 1, ∀ m, a. m ≤ n0 → firstn(m, mklist(a, n0)) = mklist(a, m) ⊦ firstn(m, a ' + mklist(a, n0)) = mklist(a, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n ≠ 0 → firstn(n, a ' + x) = a ' + firstn(n -1, x)
Proof step 9:
m ≠ 0, m ≤ n0 + 1, ∀ m, a. m ≤ n0 → firstn(m, mklist(a, n0)) = mklist(a, m) ⊦ a ' + firstn(m -1, mklist(a, n0)) = mklist(a, m)

Rule argument

spec: inst: name: firstN-rec-01 seq: ⊦ n ≠ 0 → firstn(n, a ' + x) = a ' + firstn(n -1, x) subst: [x, a, n] → [mklist(a, n0), a, m] flags: rewrite, current

Additional information

Used simplifier rules: firstN-zero: ⊦ firstn(0, x) = [];%mk-zero: ⊦ mklist(a, 0) = []; from specification list-last Used terms: mklist(a, n0), a, m