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Proof step 31 from proof prepost-write-lebs (previous step)

# avol1 = n3 + n5 + n2 + n4, # buf = (n2 + n4) * LEB_SIZE, # avol0 = # avol1, avol = avol0[n5 + n4, mapped(mkbuf(0))], lebs(avol0, n5, n4) = subarray(buf, 0, n4 * LEB_SIZE), m = 0, m0 = n5 + n4, n0 = LEB_SIZE, n1 = n4 * LEB_SIZE, n5 + n4 < # avol1, ebm-vol-inv(avol0), ebm-vol-inv(avol1), ebm-vol-inv(avol0[n5 + n4, mapped(mkbuf(0))]), is-aligned(LEB_SIZE, EB_PAGE_SIZE), mapped-full?(avol0, n5, n4), range=(avol0, 0, avol1, 0, n5), range=(avol0, n5 + n2 + n4, avol1, n5 + n2 + n4, n3), n5 + n2 + n4 ≤ # avol1, n4 * LEB_SIZE + LEB_SIZE ≤ # buf ⊦ [if m0 < # avol ∧ avol[m0].mapped? ∧ # avol[m0].data ≤ m ∧ is-aligned(m, EB_PAGE_SIZE) ∧ is-aligned(n0, EB_PAGE_SIZE) ∧ m + n0 ≤ LEB_SIZE ∧ n1 + n0 ≤ # buf then {fail_or_success#(; ; err); if err = ESUCCESS then if n0 ≠ 0 then avol[m0] := mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n0)) else choose n with n < n0 ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then avol[m0] := mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n)) ifnone skip} else abort] ( ebm-vol-inv(avol) → ⟪n := n4 + 1⟫ ( n ≤ n2 + n4 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # avol = # avol1 ∧ range=(avol, 0, avol1, 0, n5) ∧ range=(avol, n5 + n2 + n4, avol1, n5 + n2 + n4, n3) ∧ (err = ESUCCESS → lebs(avol, n5, n) = subarray(buf, 0, n * LEB_SIZE) ∧ mapped-full?(avol, n5, n)) ∧ n4 < n)), n3 + n2 = 0, n2 = 0

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 32:
# avol0 = # avol1, # buf = (n2 + n4) * LEB_SIZE, # avol1 = n3 + n5 + n2 + n4, avol = avol0[n5 + n4, mapped(mkbuf(0))], lebs(avol0, n5, n4) = subarray(buf, 0, n4 * LEB_SIZE), m = 0, m0 = n5 + n4, n0 = LEB_SIZE, n1 = n4 * LEB_SIZE, n5 + n4 < # avol1, ebm-vol-inv(avol0[n5 + n4, mapped(mkbuf(0))]), ebm-vol-inv(avol1), ebm-vol-inv(avol0), is-aligned(LEB_SIZE, EB_PAGE_SIZE), mapped-full?(avol0, n5, n4), range=(avol0, n5 + n2 + n4, avol1, n5 + n2 + n4, n3), range=(avol0, 0, avol1, 0, n5), n4 * LEB_SIZE + LEB_SIZE ≤ # buf, n5 + n2 + n4 ≤ # avol1 ⊦ [fail_or_success#(; ; err); if err = ESUCCESS then if n0 ≠ 0 then avol[m0] := mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n0)) else choose n with n < n0 ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then avol[m0] := mapped(avol[m0].data + mkempbuf(m - # avol[m0].data) + subarray(buf, n1, n)) ifnone skip] ( ebm-vol-inv(avol) → ⟪n := n4 + 1⟫ ( n ≤ n2 + n4 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # avol = # avol1 ∧ range=(avol, 0, avol1, 0, n5) ∧ range=(avol, n5 + n2 + n4, avol1, n5 + n2 + n4, n3) ∧ (err = ESUCCESS → lebs(avol, n5, n) = subarray(buf, 0, n * LEB_SIZE) ∧ mapped-full?(avol, n5, n)) ∧ n4 < n)), n3 + n2 = 0, n2 = 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ # avol[n, aleb] = # avol; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)% ⊦ is-aligned(LEB_SIZE, EB_PAGE_SIZE); (ss)% ⊦ 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)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m ≤ n → (n < m ↔ false); (s)