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Proof step 21 from proof inv-write (previous step)

m6 + # lpt = # avol, avol[m6 + m8] = mapped(buf0), avol[m2] = mapped(buf3), avol[m3] = mapped(buf2), avol[0] = mapped(buf1), m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol), ebm-vol-inv(avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))]), is-aligned(n, EB_PAGE_SIZE), is-aligned(m7, EB_PAGE_SIZE), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded(lpt, lebs(avol, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf3), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol, m5, lptlebs(# lpt, LEB_SIZE)), # buf0 ≤ m7, n2 + n ≤ # buf, m7 + n ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ n = 0, ∃ lpt0, log0. m6 + # lpt0 = # avol ∧ avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))][0].mapped? ∧ is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))][0].data) ∧ avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))][m2].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))][m2].data = logoff) ∧ is-encoded(log0, avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))][m2].data) ∧ mapped-full?(avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))], m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol[m6 + m8, mapped(buf0 + mkempbuf(m7 - # buf0) + subarray(buf, n2, n))], m5, lptlebs(# lpt0, LEB_SIZE)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
m6 + # lpt = # avol, avol[0] = mapped(buf1), avol[m3] = mapped(buf2), avol[m2] = mapped(buf3), avol[m6 + m8] = mapped(buf0), m7 = n0 + # buf0, m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol[m6 + m8, mapped(buf0 + mkempbuf(n0) + subarray(buf, n2, n))]), 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 ⊦ n = 0, ∃ lpt0, log0. m6 + # lpt0 = # avol ∧ avol[m6 + m8, mapped(buf0 + mkempbuf(n0) + subarray(buf, n2, n))][0].mapped? ∧ is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), avol[m6 + m8, mapped(buf0 + mkempbuf(n0) + subarray(buf, n2, n))][0].data) ∧ avol[m6 + m8, mapped(buf0 + mkempbuf(n0) + subarray(buf, n2, n))][m2].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m6 + m8, mapped(buf0 + mkempbuf(n0) + subarray(buf, n2, n))][m2].data = logoff) ∧ is-encoded(log0, avol[m6 + m8, mapped(buf0 + mkempbuf(n0) + subarray(buf, n2, n))][m2].data) ∧ mapped-full?(avol[m6 + m8, mapped(buf0 + mkempbuf(n0) + subarray(buf, n2, n))], m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol[m6 + m8, mapped(buf0 + mkempbuf(n0) + subarray(buf, n2, n))], m5, lptlebs(# lpt0, LEB_SIZE)))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [m7, # buf0, n0]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m7, # buf0, n0