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Proof step 121 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), 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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-copy, inst: avolume name: at-fill seq: ⊦ n < # avol → fill(avol, aleb)[n] = aleb subst: [n, aleb, avol] → [(5 + 2 * lptlebs(# lpt, LEB_SIZE)) + n, unmapped, mkavolume(# avol0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # mkavolume(n) = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s) Used terms: (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + n, unmapped, mkavolume(# avol0)