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Proof step 8 from proof reduce-initial (previous step)

# buf0 = PEB_SIZE, pebs[n] = mkpeb(buf0, m0, boolvar0), n < # pebs, ¬ boolvar0 → m0 = EB_PAGE_SIZE ∧ is-encoded(echdr(n0), subarray(buf0, 0, EB_PAGE_SIZE)), ¬ boolvar0 → m0 ≤ PEB_SIZE ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ range=(buf0, m0, emptypeb, m0, PEB_SIZE - m0), ∀ n0. n0 < # pebs → # pebs[n0].data = PEB_SIZE ∧ ( ¬ pebs[n0].bad → pebs[n0].fill ≤ PEB_SIZE ∧ is-aligned(pebs[n0].fill, EB_PAGE_SIZE) ∧ range=(pebs[n0].data, pebs[n0].fill, emptypeb, pebs[n0].fill, PEB_SIZE - pebs[n0].fill)) ∧ (¬ pebs[n0].bad → pebs[n0].fill = EB_PAGE_SIZE ∧ (∃ n. is-encoded(echdr(n), subarray(pebs[n0].data, 0, EB_PAGE_SIZE)))), ∀ n0. n0 < # pebs → # pebs[n, mkpeb(buf, m, boolvar)][n0].data = PEB_SIZE ∧ ( ¬ pebs[n, mkpeb(buf, m, boolvar)][n0].bad → pebs[n, mkpeb(buf, m, boolvar)][n0].fill ≤ PEB_SIZE ∧ is-aligned(pebs[n, mkpeb(buf, m, boolvar)][n0].fill, EB_PAGE_SIZE) ∧ range= (pebs[n, mkpeb(buf, m, boolvar)][n0].data, pebs[n, mkpeb(buf, m, boolvar)][n0].fill, emptypeb, pebs[n, mkpeb(buf, m, boolvar)][n0].fill, PEB_SIZE - pebs[n, mkpeb(buf, m, boolvar)][n0].fill)) ∧ ( ¬ pebs[n, mkpeb(buf, m, boolvar)][n0].bad → pebs[n, mkpeb(buf, m, boolvar)][n0].fill = EB_PAGE_SIZE ∧ (∃ n1. is-encoded(echdr(n1), subarray(pebs[n, mkpeb(buf, m, boolvar)][n0].data, 0, EB_PAGE_SIZE)))) ⊦ # buf = PEB_SIZE ∧ (¬ boolvar → m ≤ PEB_SIZE ∧ is-aligned(m, EB_PAGE_SIZE) ∧ range=(buf, m, emptypeb, m, PEB_SIZE - m)) ∧ (¬ boolvar → m = EB_PAGE_SIZE ∧ (∃ n. is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE))))

Heuristic quantifier applied rule all left

And obtained the following new goals

Proof step 9:
# buf0 = PEB_SIZE, pebs[n] = mkpeb(buf0, m0, boolvar0), n < # pebs, ¬ boolvar0 → m0 ≤ PEB_SIZE ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ range=(buf0, m0, emptypeb, m0, PEB_SIZE - m0), ¬ boolvar0 → m0 = EB_PAGE_SIZE ∧ is-encoded(echdr(n0), subarray(buf0, 0, EB_PAGE_SIZE)), n < # pebs → # pebs[n].data = PEB_SIZE ∧ ( ¬ pebs[n].bad → pebs[n].fill ≤ PEB_SIZE ∧ is-aligned(pebs[n].fill, EB_PAGE_SIZE) ∧ range=(pebs[n].data, pebs[n].fill, emptypeb, pebs[n].fill, PEB_SIZE - pebs[n].fill)) ∧ (¬ pebs[n].bad → pebs[n].fill = EB_PAGE_SIZE ∧ (∃ n1. is-encoded(echdr(n1), subarray(pebs[n].data, 0, EB_PAGE_SIZE)))), ∀ n0. n0 < # pebs → # pebs[n, mkpeb(buf, m, boolvar)][n0].data = PEB_SIZE ∧ ( ¬ pebs[n, mkpeb(buf, m, boolvar)][n0].bad → pebs[n, mkpeb(buf, m, boolvar)][n0].fill ≤ PEB_SIZE ∧ is-aligned(pebs[n, mkpeb(buf, m, boolvar)][n0].fill, EB_PAGE_SIZE) ∧ range= (pebs[n, mkpeb(buf, m, boolvar)][n0].data, pebs[n, mkpeb(buf, m, boolvar)][n0].fill, emptypeb, pebs[n, mkpeb(buf, m, boolvar)][n0].fill, PEB_SIZE - pebs[n, mkpeb(buf, m, boolvar)][n0].fill)) ∧ ( ¬ pebs[n, mkpeb(buf, m, boolvar)][n0].bad → pebs[n, mkpeb(buf, m, boolvar)][n0].fill = EB_PAGE_SIZE ∧ (∃ n1. is-encoded(echdr(n1), subarray(pebs[n, mkpeb(buf, m, boolvar)][n0].data, 0, EB_PAGE_SIZE)))), ∀ n0. n0 < # pebs → # pebs[n0].data = PEB_SIZE ∧ ( ¬ pebs[n0].bad → pebs[n0].fill ≤ PEB_SIZE ∧ is-aligned(pebs[n0].fill, EB_PAGE_SIZE) ∧ range=(pebs[n0].data, pebs[n0].fill, emptypeb, pebs[n0].fill, PEB_SIZE - pebs[n0].fill)) ∧ (¬ pebs[n0].bad → pebs[n0].fill = EB_PAGE_SIZE ∧ (∃ n. is-encoded(echdr(n), subarray(pebs[n0].data, 0, EB_PAGE_SIZE)))) ⊦ # buf = PEB_SIZE ∧ (¬ boolvar → m ≤ PEB_SIZE ∧ is-aligned(m, EB_PAGE_SIZE) ∧ range=(buf, m, emptypeb, m, PEB_SIZE - m)) ∧ (¬ boolvar → m = EB_PAGE_SIZE ∧ (∃ n. is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE))))

Rule argument

pos: left 6 terms: n

Additional information

Used terms: n