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Proof step 4 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

Proof step 5:
⊦ m + n < # x → restn(n, x)[m] = x[m + n]

Rule argument

spec: <toplevel> name: get-restn seq: ⊦ m + n < # x → restn(n, x)[m] = x[m + n] subst: [m, x, n] → [n, a ' + x0, m] flags: <all paths>

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic% ⊦ #(x + y) = # x + # y; (s)% ⊦ # a ' = 0 +1; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic Used terms: n, a ' + x0, m