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Proof step 57 from proof prepost-read-orphans (previous step)

m4 + # lpt = # avol, avol[m5] = mapped(buf1), avol[m1] = mapped(buf3), avol[0] = mapped(buf2), buf = mkbuf(m2 * ENCODED_NAT_SIZE), buf0 = buf, m = 0, m0 = m1, n = m2 * ENCODED_NAT_SIZE, n0 = 0, disk-layout(mksb(adr, m6, m5, m1, m2, m3, m4), # lpt), ebm-vol-inv(avol), is-encoded(mksb(adr, m6, m5, m1, m2, m3, m4), buf2), is-encoded(lpt, lebs(avol, m3, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans0, m2, buf3), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff, m0 < # avol → m0 < # avol ⊦ m0 < # avol ∧ avol[m0].mapped? ∧ n0 + n ≤ # buf0 ∧ m + n ≤ LEB_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
m4 + # lpt = # avol, avol[0] = mapped(buf2), avol[m1] = mapped(buf3), avol[m5] = mapped(buf1), LEB_SIZE < m2 * ENCODED_NAT_SIZE, m1 < # avol, disk-layout(mksb(adr, m6, m5, m1, m2, m3, m4), # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m3, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m6, m5, m1, m2, m3, m4), buf2), is-encoded-pad(orphans0, m2, buf3), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ m2 = 0

Rule argument

Additional information

Used simplifier rules: # avol = sb.main + mainareasize ⊦ disk-layout(sb, mainareasize) → # avol ≠ 0; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ ENCODED_NAT_SIZE ≠ 0; (s)% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0; (ws)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%⊦ m6 + # lpt = # avol ∧ disk-layout(mksb(adr0, m1, m2, m3, m4, m5, m6), # lpt) → ¬ # avol ≤ m3; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ mapped(buf).mapped?; (s)% ⊦ m ≤ m; (s)% ⊦ # mkbuf(n) = n; (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)