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Proof step 8 from proof prepost-read-lebs (previous step)

buf = mkbuf(m0 * m), err = ESUCCESS, m = LEB_SIZE, m0 = m2, m1 = n0, n = 0, ebm-vol-inv(avol), mapped-full?(avol, n0, m2), n0 + m2 ≤ # avol ⊦ ⟪while err = ESUCCESS ∧ n < m0 do {/* (prepost-read-lebs : invariant n ≤ m0 ∧ # buf = m0 * LEB_SIZE ∧ m1 + m0 ≤ # avol ∧ ebm-vol-inv(avol) ∧ mapped-full?(avol, m1, m0) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → subarray(buf, 0, n * LEB_SIZE) = lebs(avol, m1, n)) wfbound m0 - n) */; ebm_avol_read#(m1 + n, 0, n * m, m, avol; buf; err); n := n + 1}⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → buf = lebs(avol, n0, m2)))

Heuristic annotation applied rule annotation right

And obtained the following new goals

Proof step 9:
# buf = m0 * LEB_SIZE, buf0 = mkbuf(m0 * m), err = ESUCCESS, err0 = ESUCCESS, m = LEB_SIZE, m0 = m2, m1 = n0, n = n1, n2 = 0, n < m0, ebm-vol-inv(avol), mapped-full?(avol, n0, m2), mapped-full?(avol, m1, m0), n0 + m2 ≤ # avol, n ≤ m0, m1 + m0 ≤ # avol, err = ESUCCESS → subarray(buf, 0, n * LEB_SIZE) = lebs(avol, m1, n), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪ebm_avol_read#(m1 + n, 0, n * m, m, avol; buf; err); n := n + 1⟫ ( ( n ≤ m0 ∧ # buf = m0 * LEB_SIZE ∧ m1 + m0 ≤ # avol ∧ ebm-vol-inv(avol) ∧ mapped-full?(avol, m1, m0) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → subarray(buf, 0, n * LEB_SIZE) = lebs(avol, m1, n))) ∧ m0 - n < m0 - n1)

Rule argument

rule: invariant right arg: bound: m0 - n inv: n ≤ m0 ∧ # buf = m0 * LEB_SIZE ∧ m1 + m0 ≤ # avol ∧ ebm-vol-inv(avol) ∧ mapped-full?(avol, m1, m0) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → subarray(buf, 0, n * LEB_SIZE) = lebs(avol, m1, n)) fmapos: right 1 pos: right 1

Additional information

Used simplifier rules: ⊦ m * n = m * n0 ↔ m = 0 ∨ n = n0; (ws)% ⊦ LEB_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ n ≠ n0 → (n < n0 ↔ ¬ n0 < n); (ss)% ⊦ m < n → ¬ n < m; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ 0 ≤ m; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ 0 * n = 0; (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)% ⊦ lebs(avol, n, 0) = mkbuf(0); (s) Used formulas: n ≤ m0 ∧ # buf = m0 * LEB_SIZE ∧ m1 + m0 ≤ # avol ∧ ebm-vol-inv(avol) ∧ mapped-full?(avol, m1, m0) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → subarray(buf, 0, n * LEB_SIZE) = lebs(avol, m1, n)), m0 - n = m0 - n