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Proof step 29 from proof inv-write (previous step)

m6 + # lpt = # avol, avol[m6 + m8] = mapped(buf0), avol[0] = mapped(buf1), avol[m3] = mapped(buf2), avol[m2] = mapped(buf3), err0 = ESUCCESS, n = 0, m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol), is-aligned(m7, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol, m5, lptlebs(# lpt, LEB_SIZE)), m7 + n ≤ LEB_SIZE, n2 + n ≤ # buf, # buf0 ≤ m7, logoff ≠ LEB_SIZE → # buf3 = logoff, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ∃ lpt0, log, orphans. disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt0) ∧ m6 + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), avol[0].data) ∧ avol[m3].mapped? ∧ is-encoded-pad(orphans, m4, avol[m3].data) ∧ avol[m2].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m2].data = logoff) ∧ is-encoded(log, avol[m2].data) ∧ mapped-full?(avol, m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m5, lptlebs(# lpt0, LEB_SIZE)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
m6 + # lpt = # avol, avol[m6 + m8] = mapped(buf0), avol[0] = mapped(buf1), avol[m3] = mapped(buf2), avol[m2] = mapped(buf3), m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol), is-aligned(m7, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol, m5, lptlebs(# lpt, LEB_SIZE)), # buf0 ≤ LEB_SIZE, m7 ≤ LEB_SIZE, n2 ≤ # buf, # buf0 ≤ m7, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ∃ lpt0. m6 + # lpt0 = # avol ∧ mapped-full?(avol, m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m5, lptlebs(# lpt0, LEB_SIZE)))

Rule argument

Additional information

Used simplifier rules: ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)%m = n ⊦ disk-layout(sb, m) → disk-layout(sb, n); (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (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)