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Proof step 118 from proof inv-format (previous step)

# avol0 = # lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol = # avol0, # lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), avol[0] = mapped(buf), avol0[4] = fill(mkavolume(# avol0), unmapped)[4], avol0[3] = mapped(mkbuf(0)), avol0[2] = fill(mkavolume(# avol0), unmapped)[2], avol0[1] = mapped(mkbuf(0)), avol0[0] = fill(mkavolume(# avol0), unmapped)[0], avol[1] = mapped(mkbuf(0)), avol[3] = mapped(mkbuf(0)), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))]), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))]), ebm-vol-inv(avol0), ebm-vol-inv(avol), id○(avol, avol0, 0), is-encoded(mksb(adr, m1, 1, 3, 0, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf), is-encoded(lpt, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), range= (avol0, 5 + lptlebs(# lpt, LEB_SIZE), fill(mkavolume(# avol0), unmapped), 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE) + # lpt), 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, 5 ≤ # avol0, 5 + lptlebs(# lpt, LEB_SIZE) ≤ # avol0 ⊦ subarray(fill(mkavolume(# avol0), unmapped), 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt) = fill(mkavolume(# lpt), unmapped)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 119:
⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n])
Proof step 120:
# lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), # avol = # avol0, # avol0 = # lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE), avol[3] = mapped(mkbuf(0)), avol[1] = mapped(mkbuf(0)), avol0[0] = fill(mkavolume(# avol0), unmapped)[0], avol0[1] = mapped(mkbuf(0)), avol0[2] = fill(mkavolume(# avol0), unmapped)[2], avol0[3] = mapped(mkbuf(0)), avol0[4] = fill(mkavolume(# avol0), unmapped)[4], avol[0] = mapped(buf), ebm-vol-inv(avol), ebm-vol-inv(avol0), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))]), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))]), id○(avol, avol0, 0), is-encoded(lpt, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, 1, 3, 0, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), range= (avol0, 5 + lptlebs(# lpt, LEB_SIZE), fill(mkavolume(# avol0), unmapped), 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE) + # lpt), 5 + lptlebs(# lpt, LEB_SIZE) ≤ # avol0, 5 ≤ # avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0 ⊦ # subarray(fill(mkavolume(# avol0), unmapped), 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt) = # fill(mkavolume(# lpt), unmapped) ∧ (∀ n. n < # subarray(fill(mkavolume(# avol0), unmapped), 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt) → subarray(fill(mkavolume(# avol0), unmapped), 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt)[n] = fill(mkavolume(# lpt), unmapped)[n])

Rule argument

spec: array, inst: avolume name: Extension seq: ⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n]) subst: [avol0, avol] → [fill(mkavolume(# lpt), unmapped), subarray (fill(mkavolume(# avol0), unmapped), 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt)] flags: <all paths>

Additional information

Used terms: fill(mkavolume(# lpt), unmapped), subarray (fill(mkavolume(# avol0), unmapped), 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt)