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Proof step 349 from proof refine-write (previous step)

⟨fail_or_success#(; ; err)⟩ (err = ESUCCESS), # apebs = # wlar, vols[v][vtblpnum3] = ⌜n4⌝ , avols[v][vtblpnum3] = mapped(buf2, m), wlar[n4] = wl-entry(m1, used), apebs[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), n0 ≠ 0, vtblpnum4 ≠ n4, aehdr.valid?, avhdr.valid?, vtblpnum3 < # vols[v], n4 < # wlar, vtblpnum3 < # avols[v], abs(avols, apebs, vols, q), abs (avols[v, avols[v][vtblpnum3, mapped((subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n0)) + mkempbuf(LEB_SIZE - vtblpnum5 + n0), vtblpnum5 + n0)]], apebs0, vols0, q0), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(vtblpnum5, EB_PAGE_SIZE), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), v ∈ avols, v ∈ vols, n3 + n0 ≤ # buf0, vtblpnum5 ≤ LEB_SIZE, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, n0 + n3 ≤ # buf0, m ≤ vtblpnum5, m0 ≤ vtblpnum5, vtblpnum5 + n0 ≤ LEB_SIZE, ⌊err3⌋ , ¬ VTBL_VOLID ∈ vols ⊦ ∃ err0. (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ⟨err := err0; if err = ESUCCESS then if avols[v][vtblpnum3].mapped? then if n0 ≠ 0 then avols[v][vtblpnum3] := mapped (subarray(avols[v][vtblpnum3].data, 0, vtblpnum5) + subarray(buf0, n3, n0) + mkempbuf(LEB_SIZE - vtblpnum5 - n0), vtblpnum5 + n0) else avols[v][vtblpnum3] := mapped(mkempbuf(vtblpnum5) + subarray(buf0, n3, n0) + mkempbuf(LEB_SIZE - vtblpnum5 - n0), vtblpnum5 + n0) else if avols[v][vtblpnum3].mapped? then choose n1 with n1 < n0 ∧ is-aligned(n1, EB_PAGE_SIZE) in if n1 ≠ 0 then avols[v][vtblpnum3] := mapped (subarray(avols[v][vtblpnum3].data, 0, vtblpnum5) + subarray(buf0, n3, n1) + mkempbuf(LEB_SIZE - vtblpnum5 - n1), vtblpnum5 + n1) ifnone skip else if n0 ≠ 0 then avols[v][vtblpnum3] := unmapped⟩ (abs(avols, apebs0, vols0, q0) ∧ ESUCCESS = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 350:
⟨fail_or_success#(; ; err)⟩ (err = ESUCCESS), # apebs = # wlar, LEB_SIZE = n2 + vtblpnum5 + n0, apebs[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), wlar[n4] = wl-entry(m1, used), avols[v][vtblpnum3] = mapped(buf2, m), vols[v][vtblpnum3] = ⌜n4⌝ , avhdr.valid?, aehdr.valid?, vtblpnum3 < # avols[v], n4 < # wlar, vtblpnum3 < # vols[v], abs(avols[v, avols[v][vtblpnum3, mapped((subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n0)) + mkempbuf(n2), vtblpnum5 + n0)]], apebs0, vols0, q0), abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n0, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, vtblpnum5 + n0 ≤ LEB_SIZE, m0 ≤ vtblpnum5, m ≤ vtblpnum5, n0 + n3 ≤ # buf0, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, n3 + n0 ≤ # buf0, ⌊err3⌋ ⊦ ∃ err0. (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ⟨err := err0; if err = ESUCCESS then if avols[v][vtblpnum3].mapped? then if n0 ≠ 0 then avols[v][vtblpnum3] := mapped (subarray(avols[v][vtblpnum3].data, 0, vtblpnum5) + subarray(buf0, n3, n0) + mkempbuf(LEB_SIZE - vtblpnum5 - n0), vtblpnum5 + n0) else avols[v][vtblpnum3] := mapped(mkempbuf(vtblpnum5) + subarray(buf0, n3, n0) + mkempbuf(LEB_SIZE - vtblpnum5 - n0), vtblpnum5 + n0) else if avols[v][vtblpnum3].mapped? then choose n1 with n1 < n0 ∧ is-aligned(n1, EB_PAGE_SIZE) in if n1 ≠ 0 then avols[v][vtblpnum3] := mapped (subarray(avols[v][vtblpnum3].data, 0, vtblpnum5) + subarray(buf0, n3, n1) + mkempbuf(LEB_SIZE - vtblpnum5 - n1), vtblpnum5 + n1) ifnone skip else if n0 ≠ 0 then avols[v][vtblpnum3] := unmapped⟩ (abs(avols, apebs0, vols0, q0) ∧ ESUCCESS = err), n0 = 0, vtblpnum4 = n4, VTBL_VOLID ∈ vols

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE, vtblpnum5 + n0, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE, vtblpnum5 + n0, n