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Proof step 114 from proof refine-read (previous step)

# vols[avhdr.vol] = # avols[avhdr.vol], # apebs = # wlar, wlar[n1].status = used, apebs[n1] = mkpeb(aehdr, avhdr, buf1, m, true), vols[avhdr.vol][avhdr.leb] = ⌜n1⌝ , avols[avhdr.vol][avhdr.leb] = mapped(buf1, m0), avhdr.valid?, avhdr.leb < # avols[avhdr.vol], n1 < # wlar, bflipset-cons(bflipset, wlar), ebm-cons(avols), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m, true)), unique-sqns(apebs), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs, wlar), avhdr.vol ∈ vols, avhdr.vol ∈ avols, m ≤ m0, n0 + n ≤ # buf2, vtblpnum4 + n ≤ LEB_SIZE ⊦ n1 = vtblpnum3, VTBL_VOLID ∈ vols

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 115:
# apebs = # wlar, # vols[v] = # avols[v], wlar[n1].status = used, avols[v][m1] = mapped(buf1, m0), vols[v][m1] = ⌜n1⌝ , apebs[n1] = mkpeb(aehdr, avhdr, buf1, m, true), avhdr = avidhdr(v, m1, m2, m3, m4), avhdr.valid?, n1 < # wlar, m1 < # avols[v], bflipset-cons(bflipset, wlar), ebm-cons(avols), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m, true)), unique-sqns(apebs), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs, wlar), v ∈ avols, v ∈ vols, vtblpnum4 + n ≤ LEB_SIZE, n0 + n ≤ # buf2, m ≤ m0 ⊦ n1 = vtblpnum3, VTBL_VOLID ∈ vols

Rule argument

spec: avidheader name: elim seq: ⊦ avhdr.valid? → ( ( ((v = avhdr.vol ∧ m = avhdr.leb) ∧ m0 = avhdr.sqn) ∧ m1 = avhdr.size) ∧ m2 = avhdr.checksum ↔ avhdr = avidhdr(v, m, m0, m1, m2)) subst: [avhdr, v, m, m0, m1, m2] → [avhdr, v, m1, m2, m3, m4]

Additional information

Used simplifier rules: ⊦ avhdr.valid? → ( ( ((v = avhdr.vol ∧ m = avhdr.leb) ∧ m0 = avhdr.sqn) ∧ m1 = avhdr.size) ∧ m2 = avhdr.checksum ↔ avhdr = avidhdr(v, m, m0, m1, m2)); (elim) Used terms: avhdr, v, m1, m2, m3, m4