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Proof step 12 from proof reduce-initial (previous step)

apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0), n0 < # apebs, n < # apebs ∧ # buf0 = LEB_SIZE ∧ ( ¬ boolvar0 → (aehdr0 = empty → avhdr0 = empty) ∧ (aehdr0 ≠ garbage ∧ avhdr0 = empty → m0 = 0) ∧ m0 ≤ LEB_SIZE ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ subarray(buf0, m0, LEB_SIZE - m0) = mkempbuf(LEB_SIZE - m0)) ∧ (¬ boolvar0 → aehdr0.valid? ∧ avhdr0 = empty) → # buf = LEB_SIZE ∧ ( ¬ boolvar → (aehdr = empty → avhdr = empty) ∧ (aehdr ≠ garbage ∧ avhdr = empty → m = 0) ∧ m ≤ LEB_SIZE ∧ is-aligned(m, EB_PAGE_SIZE) ∧ subarray(buf, m, LEB_SIZE - m) = mkempbuf(LEB_SIZE - m)) ∧ (¬ boolvar → aehdr.valid? ∧ avhdr = empty), ∀ n0. n0 < # apebs → # apebs[n0].data = LEB_SIZE ∧ ( ¬ apebs[n0].bad → (apebs[n0].echdr = empty → apebs[n0].vidhdr = empty) ∧ (apebs[n0].echdr ≠ garbage ∧ apebs[n0].vidhdr = empty → apebs[n0].fill = 0) ∧ apebs[n0].fill ≤ LEB_SIZE ∧ is-aligned(apebs[n0].fill, EB_PAGE_SIZE) ∧ subarray(apebs[n0].data, apebs[n0].fill, LEB_SIZE - apebs[n0].fill) = mkempbuf(LEB_SIZE - apebs[n0].fill)) ∧ (¬ apebs[n0].bad → apebs[n0].echdr.valid? ∧ apebs[n0].vidhdr = empty) ⊦ # apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].data = LEB_SIZE ∧ ( ¬ apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].bad → (apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].echdr = empty → apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].vidhdr = empty) ∧ ( apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].echdr ≠ garbage ∧ apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].vidhdr = empty → apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].fill = 0) ∧ apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].fill ≤ LEB_SIZE ∧ is-aligned(apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].fill, EB_PAGE_SIZE) ∧ subarray (apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].data, apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].fill, LEB_SIZE - apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].fill) = mkempbuf(LEB_SIZE - apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].fill)) ∧ ( ¬ apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].bad → apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].echdr.valid? ∧ apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0].vidhdr = empty)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0), apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0] = mkpeb(aehdr1, avhdr1, buf1, m1, boolvar1), n0 < # apebs, n < # apebs ∧ # buf0 = LEB_SIZE ∧ ( ¬ boolvar0 → (aehdr0 = empty → avhdr0 = empty) ∧ (aehdr0 ≠ garbage ∧ avhdr0 = empty → m0 = 0) ∧ m0 ≤ LEB_SIZE ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ subarray(buf0, m0, LEB_SIZE - m0) = mkempbuf(LEB_SIZE - m0)) ∧ (¬ boolvar0 → aehdr0.valid? ∧ avhdr0 = empty) → # buf = LEB_SIZE ∧ ( ¬ boolvar → (aehdr = empty → avhdr = empty) ∧ (aehdr ≠ garbage ∧ avhdr = empty → m = 0) ∧ m ≤ LEB_SIZE ∧ is-aligned(m, EB_PAGE_SIZE) ∧ subarray(buf, m, LEB_SIZE - m) = mkempbuf(LEB_SIZE - m)) ∧ (¬ boolvar → aehdr.valid? ∧ avhdr = empty), ∀ n0. n0 < # apebs → # apebs[n0].data = LEB_SIZE ∧ ( ¬ apebs[n0].bad → (apebs[n0].echdr = empty → apebs[n0].vidhdr = empty) ∧ (apebs[n0].echdr ≠ garbage ∧ apebs[n0].vidhdr = empty → apebs[n0].fill = 0) ∧ apebs[n0].fill ≤ LEB_SIZE ∧ is-aligned(apebs[n0].fill, EB_PAGE_SIZE) ∧ subarray(apebs[n0].data, apebs[n0].fill, LEB_SIZE - apebs[n0].fill) = mkempbuf(LEB_SIZE - apebs[n0].fill)) ∧ (¬ apebs[n0].bad → apebs[n0].echdr.valid? ∧ apebs[n0].vidhdr = empty) ⊦ # buf1 = LEB_SIZE ∧ ( ¬ boolvar1 → (aehdr1 = empty → avhdr1 = empty) ∧ (aehdr1 ≠ garbage ∧ avhdr1 = empty → m1 = 0) ∧ m1 ≤ LEB_SIZE ∧ is-aligned(m1, EB_PAGE_SIZE) ∧ subarray(buf1, m1, LEB_SIZE - m1) = mkempbuf(LEB_SIZE - m1)) ∧ (¬ boolvar1 → aehdr1.valid? ∧ avhdr1 = empty)

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0], aehdr1, avhdr1, buf1, m1, boolvar1]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[n, mkpeb(aehdr, avhdr, buf, m, boolvar)][n0], aehdr1, avhdr1, buf1, m1, boolvar1