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Proof step 17 from proof inv-erase (previous step)

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))

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: n = m

Additional information

Used simplifier rules: ⊦ m ≠ n → pebs[n, peb][m] = pebs[m]; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # pebs ⊦ pebs[n] = mkpeb(buf, m, boolvar) ∧ mtd-cons(pebs) → # buf = PEB_SIZE; (s)%⊦ mkpeb(buf, m, boolvar) = mkpeb(buf0, m0, boolvar0) ↔ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (ws)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < # pebs → pebs[m, peb][m] = peb; (s)% ⊦ # emptypeb = PEB_SIZE; (s)% ⊦ 0 ≤ m; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)% ⊦ m - 0 = m; (s)% ⊦ range=(buf, n, buf, n, m) ↔ n + m ≤ # buf; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m; (s) Used formulas: n = m