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Proof step 120 from proof inv-format (previous step)

# 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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 121:
# 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), n < # lpt, 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 ⊦ fill(mkavolume(# avol0), unmapped)[(5 + 2 * lptlebs(# lpt, LEB_SIZE)) + n] = unmapped

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → fill(mkavolume(n), aleb)[m] = aleb; (s)% ⊦ n0 < n → subarray(avol, m, n)[n0] = avol[m + n0]; (s)% ⊦ # mkavolume(n) = n; (s)% ⊦ # fill(avol, aleb) = # avol; (s)% ⊦ # subarray(avol, m, n) = n; (s)