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Proof step 9 from proof firstn-last-rec (previous step)

m ≤ # y0, ∀ x0. m < # x0 → x0.first ' + firstn(m, x0.rest) = firstn(m, x0) + x0[m] ' ⊦ a ' + firstn(m, y0) = firstn(m, a ' + y0) + (a ' + y0)[m] '

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: a ' + y0

Additional information

Used simplifier rules: len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%a: ⊦ (x + y) + z = x + y + z; from specification list%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%c-08: ⊦ (a ' + x).first = a; from specification list%c-07: ⊦ (a ' + x).rest = x; from specification list Used terms: a ' + y0