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Proof step 51 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), m = m7, m0 = m8, sb = mksb(adr, m1, m2, m3, m4, m5, m6), sb.main + m0 < # avol, 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)), # buf0 ≤ m7, m7 + n ≤ LEB_SIZE, n0 + n ≤ # buf, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ sb.main + m0 < # avol ∧ (avol[sb.main + m0].mapped? → avol[sb.main + m0].mapped? ∧ sb.main + m0 < # avol)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (s)