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Proof step 16 from proof inv-unmap (previous step)

m5 + # lpt = # avol, avol[0] = mapped(buf), avol[m2] = mapped(buf0), avol[m1] = mapped(buf1), m6 < # lpt, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ 0 = m5 + m6, m1 = m5 + m6, (∃ lpt0. m5 + # lpt0 = # avol ∧ mapped-full?(avol[m5 + m6, unmapped], m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol[m5 + m6, unmapped], m4, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol[m5 + m6, unmapped])

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 17:
m5 + # lpt = # avol, avol[m1] = mapped(buf1), avol[m2] = mapped(buf0), avol[0] = mapped(buf), m6 < # lpt, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol), ebm-vol-inv(avol[m5 + m6, unmapped]), is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), buf), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ 0 = m5 + m6, m1 = m5 + m6, (∃ lpt0. m5 + # lpt0 = # avol ∧ mapped-full?(avol[m5 + m6, unmapped], m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol[m5 + m6, unmapped], m4, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol[m5 + m6, unmapped])

Rule argument

fma: ebm-vol-inv(avol[m5 + m6, unmapped])

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)%n < # avol ⊦ ebm-vol-inv(avol) → ( ebm-vol-inv(avol[n, aleb]) ↔ ( avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE)) → aleb.mapped? → # aleb.data ≤ LEB_SIZE ∧ is-aligned(# aleb.data, EB_PAGE_SIZE)); (ss)% ⊦ ¬ unmapped.mapped?; (s) Used formulas: ebm-vol-inv(avol[m5 + m6, unmapped])