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Proof step 16 from proof put-firstn-restn (previous step)

# y0 = m + 1 ⊦ (y0 + z)[m, a] = firstn(m, y0) + a ' + z, y0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ n < # x → (x + y)[n, a] = x[n, a] + y
Proof step 18:
# y0 = m + 1, m < # y0 ⊦ y0[m, a] + z = firstn(m, y0) + a ' + z, y0 = []

Rule argument

spec: <toplevel> name: put-app-left seq: ⊦ n < # x → (x + y)[n, a] = x[n, a] + y subst: [a, n, y, x] → [a, m, z, y0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = n + 1 → ¬ m ≤ n; (s) Used terms: a, m, z, y0