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Proof step 48 from proof prepost-read-superblock (previous step)

avol[0] = mapped(buf1), buf = mkbuf(LEB_SIZE), err = err0, err = ESUCCESS, ebm-vol-inv(avol), is-encoded(sb0, buf1), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ # avol = 0, (0 + LEB_SIZE ≤ #(avol[0].data + mkempbuf(LEB_SIZE - # avol[0].data)) ∧ 0 + LEB_SIZE ≤ # buf) ∧ (avol[0].mapped? ∧ 0 < # avol) ∧ LEB_SIZE ≥ # avol[0].data ∧ avol[0].mapped? ∧ 0 < # avol

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
avol[0] = mapped(buf1), LEB_SIZE < # buf1, ebm-vol-inv(avol), is-encoded(sb0, buf1), LEB_SIZE ≤ # buf1 + (LEB_SIZE - # buf1) ⊦ # avol = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ¬ n + (m - n) < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ m ≤ m; (s)% ⊦ # mkbuf(n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)