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Proof step 3 from proof restn-at (previous step)

m + n ≤ # x0, ∀ m, n. m + n < # x0 → restn(m, x0)[n] = x0[m + n] ⊦ restn(m, a ' + x0)[n] = (a ' + x0)[m + n]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del inst: name: get-restn seq: ⊦ m + n < # x → restn(n, x)[m] = x[m + n] subst: [m, x, n] → [n, a ' + x0, m] flags: rewrite, current

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic2%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 Used terms: n, a ' + x0, m