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Proof step 10 from proof prepost-write-lebs (previous step)

# avol = # avol1, # buf = m2 * LEB_SIZE, lebs(avol, n0, n1) = subarray(buf, 0, n1 * LEB_SIZE), m2 = n2 + n1, n1 < m2, ebm-vol-inv(avol), ebm-vol-inv(avol1), mapped-full?(avol, n0, n1), range=(avol, n0 + m2, avol1, n0 + m2, # avol1 - n0 + m2), range=(avol, 0, avol1, 0, n0), n0 + m2 ≤ # avol1, n1 ≤ m2 ⊦ ⟪ebm_avol_remap#(n0 + n1; avol; err); n := n1; if err = ESUCCESS then ebm_avol_write#(n0 + n, 0, n * LEB_SIZE, LEB_SIZE, buf; avol; err); n := n + 1⟫ ( n ≤ m2 ∧ ebm-vol-inv(avol) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # avol = # avol1 ∧ range=(avol, 0, avol1, 0, n0) ∧ range=(avol, n0 + m2, avol1, n0 + m2, # avol1 - n0 + m2) ∧ (err = ESUCCESS → lebs(avol, n0, n) = subarray(buf, 0, n * LEB_SIZE) ∧ mapped-full?(avol, n0, n)) ∧ m2 < n2 + n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
# buf = (n2 + n1) * LEB_SIZE, # avol = # avol1, lebs(avol, n0, n1) = subarray(buf, 0, n1 * LEB_SIZE), n2 ≠ 0, ebm-vol-inv(avol1), ebm-vol-inv(avol), mapped-full?(avol, n0, n1), range=(avol, 0, avol1, 0, n0), range=(avol, n0 + n2 + n1, avol1, n0 + n2 + n1, # avol1 - n0 + n2 + n1), n0 + n2 + n1 ≤ # avol1 ⊦ ⟪ebm_avol_remap#(n0 + n1; avol; err); n := n1; if err = ESUCCESS then ebm_avol_write#(n0 + n, 0, n * LEB_SIZE, LEB_SIZE, buf; avol; err); n := n + 1⟫ ( n ≤ n2 + n1 ∧ ebm-vol-inv(avol) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # avol = # avol1 ∧ range=(avol, 0, avol1, 0, n0) ∧ range=(avol, n0 + n2 + n1, avol1, n0 + n2 + n1, # avol1 - n0 + n2 + n1) ∧ (err = ESUCCESS → lebs(avol, n0, n) = subarray(buf, 0, n * LEB_SIZE) ∧ mapped-full?(avol, n0, n)) ∧ n1 < n)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → m ≤ n; (s)