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Proof step 10 from proof reduce (previous step)

# buf0 = LEB_SIZE, apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0), n < # apebs, ¬ 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), ∀ n0. n0 < # apebs → # 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)) ⊦ # 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))

User applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: n abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s) Used terms: n