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Proof step 49 from proof inv-write (previous step)

PEB_SIZE = n0 + m1, PEB_SIZE = n3 + m2 + n1, pebs[m3] = mkpeb(buf0, m1, false), n4 < n3, m3 < # pebs, n1 < n, is-aligned(m1, EB_PAGE_SIZE), is-aligned(n1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(m2, EB_PAGE_SIZE), mtd-cons(pebs), range=(buf0, m1, emptypeb, m1, n0), m1 ≤ PEB_SIZE, m2 + n1 ≤ PEB_SIZE, n2 + n ≤ # buf, m2 + n ≤ PEB_SIZE, m1 ≤ m2, n2 + n1 ≤ # buf, ⌊err0⌋ ⊦ copy(buf, n2, buf0, m2, n1)[(m2 + n1) + n4] = empty, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ m0 < # buf → copy(buf0, n, buf, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ buf[m0];buf0[m0 + n - n0])
Proof step 51:
PEB_SIZE = n3 + m2 + n1, PEB_SIZE = n0 + m1, pebs[m3] = mkpeb(buf0, m1, false), n1 < n, m3 < # pebs, n4 < n3, (m2 + n1) + n4 < # buf0, is-aligned(m2, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n1, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), mtd-cons(pebs), range=(buf0, m1, emptypeb, m1, n0), n2 + n1 ≤ # buf, m1 ≤ m2, m2 + n ≤ PEB_SIZE, n2 + n ≤ # buf, m2 + n1 ≤ PEB_SIZE, m1 ≤ PEB_SIZE, ⌊err0⌋ ⊦ ((m2 + n1) + n4 < m2 ∨ m2 + n1 ≤ (m2 + n1) + n4 ⊃ buf0[(m2 + n1) + n4];buf[((m2 + n1) + n4) + n2 - m2]) = empty, n1 = 0

Rule argument

spec: array-copy, inst: buffer name: at-copy seq: ⊦ m0 < # buf → copy(buf0, n, buf, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ buf[m0];buf0[m0 + n - n0]) subst: [m0, m, n0, buf, n, buf0] → [(m2 + n1) + n4, n1, m2, buf0, n2, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # pebs ⊦ pebs[n] = mkpeb(buf, m, boolvar) ∧ mtd-cons(pebs) → # buf = PEB_SIZE; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s) Used terms: (m2 + n1) + n4, n1, m2, buf0, n2, buf