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Proof step 93 from proof inv-commit (previous step)

# avol2 = # avol0, # avol = # avol0, # lpt0 = # lpt, # lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol2[0] = mapped(buf3), avol0[0] = mapped(buf2), avol0[3] = mapped(buf0), avol0[1] = mapped(buf1), 4 < # avol0, 2 < # avol0, ebm-vol-inv(avol2), ebm-vol-inv(avol0[2, mapped(mkbuf(0))]), ebm-vol-inv(avol0), ebm-vol-inv(avol0[2, mapped(mkbuf(0))][4, mapped(buf)]), ebm-vol-inv(avol), id○(avol2, avol, 0), is-encoded(mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf3), is-encoded(lpt, lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded(lpt0, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf2), is-encoded-pad(orphans0, m6, buf0), is-encoded-pad(orphans, # orphans, buf), mapped-full?(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), range=(avol, 0, avol0[2, mapped(mkbuf(0))][4, mapped(buf)], 0, 5 + lptlebs(# lpt, LEB_SIZE)), range=(avol, 5 + 2 * lptlebs(# lpt, LEB_SIZE), avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt), 2 * lptlebs(# lpt, LEB_SIZE) + 5 ≤ # avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ (∃ lpt1, log0. lptlebs(# lpt, LEB_SIZE) = lptlebs(# lpt1, LEB_SIZE) ∧ 2 * lptlebs(# lpt, LEB_SIZE) = 2 * lptlebs(# lpt1, LEB_SIZE) ∧ (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt1 = # avol0 ∧ avol2[4].mapped? ∧ avol2[2].mapped? ∧ # avol2[2].data = 0 ∧ is-encoded(log0, avol2[2].data) ∧ mapped-full?(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol2, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)))) ∧ avol2[2].data = mkbuf(0) ∧ is-encoded-pad(orphans, # orphans, avol2[4].data)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 94:
⊦ avol[n] = aleb → (id○(avol, avol0, n) ↔ avol = avol0[n, aleb])
Proof step 95:
# lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), # lpt0 = # lpt, # avol = # avol0, # avol2 = # avol0, (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol0[1] = mapped(buf1), avol0[3] = mapped(buf0), avol0[0] = mapped(buf2), avol2[0] = mapped(buf3), avol2 = avol[0, mapped(buf3)], 2 < # avol0, 4 < # avol0, ebm-vol-inv(avol), ebm-vol-inv(avol0[2, mapped(mkbuf(0))][4, mapped(buf)]), ebm-vol-inv(avol0), ebm-vol-inv(avol0[2, mapped(mkbuf(0))]), ebm-vol-inv(avol2), is-encoded(mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf2), is-encoded(lpt0, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m3, 2, 4, # orphans, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf3), is-encoded-pad(orphans, # orphans, buf), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), mapped-full?(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)), range=(avol, 5 + 2 * lptlebs(# lpt, LEB_SIZE), avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt), range=(avol, 0, avol0[2, mapped(mkbuf(0))][4, mapped(buf)], 0, 5 + lptlebs(# lpt, LEB_SIZE)), 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, 2 * lptlebs(# lpt, LEB_SIZE) + 5 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ (∃ lpt1, log0. lptlebs(# lpt, LEB_SIZE) = lptlebs(# lpt1, LEB_SIZE) ∧ 2 * lptlebs(# lpt, LEB_SIZE) = 2 * lptlebs(# lpt1, LEB_SIZE) ∧ (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt1 = # avol0 ∧ avol2[4].mapped? ∧ avol2[2].mapped? ∧ # avol2[2].data = 0 ∧ is-encoded(log0, avol2[2].data) ∧ mapped-full?(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol2, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)))) ∧ avol2[2].data = mkbuf(0) ∧ is-encoded-pad(orphans, # orphans, avol2[4].data)

Rule argument

spec: array-copy, inst: avolume name: idexcept-extract-left seq: ⊦ avol[n] = aleb → (id○(avol, avol0, n) ↔ avol = avol0[n, aleb]) subst: [aleb, n, avol0, avol] → [mapped(buf3), 0, avol, avol2] flags: <all paths>

Additional information

Used terms: mapped(buf3), 0, avol, avol2