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Proof step 16 from proof inv-erase (previous step)

pebs[n] = mkpeb(buf0, m1, boolvar), pebs[m] = mkpeb(buf, m0, false), n < # pebs, m < # pebs, mtd-cons(pebs), ¬ boolvar → m1 ≤ PEB_SIZE ∧ is-aligned(m1, EB_PAGE_SIZE) ∧ range=(buf0, m1, emptypeb, m1, PEB_SIZE - m1) ⊦ # pebs[m, mkpeb(emptypeb, 0, false)][n].data = PEB_SIZE ∧ ( ¬ pebs[m, mkpeb(emptypeb, 0, false)][n].bad → pebs[m, mkpeb(emptypeb, 0, false)][n].fill ≤ PEB_SIZE ∧ is-aligned(pebs[m, mkpeb(emptypeb, 0, false)][n].fill, EB_PAGE_SIZE) ∧ range= (pebs[m, mkpeb(emptypeb, 0, false)][n].data, pebs[m, mkpeb(emptypeb, 0, false)][n].fill, emptypeb, pebs[m, mkpeb(emptypeb, 0, false)][n].fill, PEB_SIZE - pebs[m, mkpeb(emptypeb, 0, false)][n].fill))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
pebs[m] = mkpeb(buf, m0, false), pebs[n] = mkpeb(buf0, m1, boolvar), pebs[m, mkpeb(emptypeb, 0, false)][n] = mkpeb(buf1, m2, boolvar0), m < # pebs, n < # pebs, mtd-cons(pebs), ¬ boolvar → m1 ≤ PEB_SIZE ∧ is-aligned(m1, EB_PAGE_SIZE) ∧ range=(buf0, m1, emptypeb, m1, PEB_SIZE - m1) ⊦ # buf1 = PEB_SIZE ∧ (¬ boolvar0 → m2 ≤ PEB_SIZE ∧ is-aligned(m2, EB_PAGE_SIZE) ∧ range=(buf1, m2, emptypeb, m2, PEB_SIZE - m2))

Rule argument

spec: peb name: elim seq: ⊦ (buf = peb.data ∧ m = peb.fill) ∧ (boolvar ↔ peb.bad) ↔ peb = mkpeb(buf, m, boolvar) subst: [peb, buf, m, boolvar] → [pebs[m, mkpeb(emptypeb, 0, false)][n], buf1, m2, boolvar0]

Additional information

Used simplifier rules: ⊦ (buf = peb.data ∧ m = peb.fill) ∧ (boolvar ↔ peb.bad) ↔ peb = mkpeb(buf, m, boolvar); (elim) Used terms: pebs[m, mkpeb(emptypeb, 0, false)][n], buf1, m2, boolvar0