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Proof step 20 from proof reduce-initial (previous step)

# buf0 = PEB_SIZE, PEB_SIZE = n2 + EB_PAGE_SIZE, pebs[n] = mkpeb(buf0, m0, boolvar0), n < # pebs, EB_PAGE_SIZE ≤ PEB_SIZE, (¬ boolvar0 → m0 = EB_PAGE_SIZE ∧ (∃ n0. is-encoded(echdr(n0), subarray(buf0, 0, EB_PAGE_SIZE)))) → # buf1 = PEB_SIZE ∧ EB_PAGE_SIZE ≤ PEB_SIZE ∧ range=(buf1, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, n2) ∧ m1 = EB_PAGE_SIZE ∧ is-encoded(echdr(n1), subarray(buf1, 0, EB_PAGE_SIZE)), ¬ 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)), ∀ 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)))) ⊦ m1 = EB_PAGE_SIZE ∧ (∃ n1. is-encoded(echdr(n1), subarray(buf1, 0, EB_PAGE_SIZE)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# buf0 = PEB_SIZE, pebs[n] = mkpeb(buf0, m0, boolvar0), n < # pebs, EB_PAGE_SIZE ≤ PEB_SIZE, (¬ boolvar0 → m0 = EB_PAGE_SIZE ∧ (∃ n0. is-encoded(echdr(n0), subarray(buf0, 0, EB_PAGE_SIZE)))) → # buf1 = PEB_SIZE ∧ range=(buf1, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, LEB_SIZE + EB_PAGE_SIZE) ∧ m1 = EB_PAGE_SIZE ∧ is-encoded(echdr(n1), subarray(buf1, 0, EB_PAGE_SIZE)), ¬ 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)), ∀ 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)))) ⊦ m1 = EB_PAGE_SIZE ∧ (∃ n1. is-encoded(echdr(n1), subarray(buf1, 0, EB_PAGE_SIZE)))

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ LEB_SIZE + 2 * EB_PAGE_SIZE = PEB_SIZE; (s)% ⊦ m + m = 2 * m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%pebsize-minus-eb-page-size: ⊦ PEB_SIZE = n + EB_PAGE_SIZE → n = LEB_SIZE + EB_PAGE_SIZE; (forward) from specification eraseblock