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Proof step 146 from proof inv-format (previous step)

# pebs0 = n0 + m1, # pebs = n0 + m1, pebs[m1] = mkpeb(buf, m, true), mtd-cons(pebs0), mtd-cons(pebs), n ≤ m1, n < m1 → ubi-io-peb-initial(pebs[n]) ⊦ n0 = 0, ubi-io-peb-initial(subarray(pebs, 0, m1 + 1)[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 147:
⊦ n0 < n → subarray(pebs, m, n)[n0] = pebs[m + n0]
Proof step 148:
# pebs = n0 + m1, # pebs0 = n0 + m1, pebs[m1] = mkpeb(buf, m, true), n < m1 + 1, mtd-cons(pebs), mtd-cons(pebs0), n ≤ m1, n < m1 → ubi-io-peb-initial(pebs[n]) ⊦ n0 = 0, ubi-io-peb-initial(pebs[0 + n])

Rule argument

spec: array-copy, inst: pebs name: subarray-at seq: ⊦ n0 < n → subarray(pebs, m, n)[n0] = pebs[m + n0] subst: [n0, n, m, pebs] → [n, m1 + 1, 0, pebs] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%# pebs = n ⊦ subarray(pebs, 0, n) = pebs; (s) Used terms: n, m1 + 1, 0, pebs