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Proof step 43 from proof refine-read-vidhdr (previous step)

apebs[m2] = mkpeb(aehdr, avhdr1, buf0, m1, false), pebs[m2] = mkpeb(buf1, m, false), subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE) ≠ emptypage, m2 < # pebs, m2 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, m, false), mkpeb(aehdr, avhdr1, buf0, m1, false)), mtd-cons(pebs), ubi-io-inv(apebs), 2 * EB_PAGE_SIZE ≤ PEB_SIZE ⊦ ⟪decode_vidheader#(EB_PAGE_SIZE, subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE); vhdr; err); avhdr := avhdr0; if err = ESUCCESS then avhdr := avidhdr(vhdr.vol, vhdr.leb, vhdr.sqn, vhdr.size, vhdr.checksum)⟫ ⟨aubi_io_read_vidhdr#(m2, apebs; avhdr0; isbad, err0)⟩ (avhdr = avhdr0 ∧ (bitflips ↔ isbad) ∧ err = err0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 44:
EB_PAGE_SIZE ≤ # buf ⊦ ⟪decode_vidheader#(EB_PAGE_SIZE, buf; vhdr; err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded(vhdr, subarray(buf, 0, EB_PAGE_SIZE))))
Proof step 45:
pebs[m2] = mkpeb(buf1, m, false), apebs[m2] = mkpeb(aehdr, avhdr1, buf0, m1, false), buf2 = subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), m2 < # apebs, m2 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, m, false), mkpeb(aehdr, avhdr1, buf0, m1, false)), mtd-cons(pebs), ubi-io-inv(apebs), 2 * EB_PAGE_SIZE ≤ PEB_SIZE, EB_PAGE_SIZE ≤ # subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE) ⊦ [decode_vidheader#(EB_PAGE_SIZE, subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE); vhdr; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded(vhdr, subarray(buf2, 0, EB_PAGE_SIZE))) → ⟪avhdr := avhdr0; if err = ESUCCESS then avhdr := avidhdr(vhdr.vol, vhdr.leb, vhdr.sqn, vhdr.size, vhdr.checksum)⟫ ⟨aubi_io_read_vidhdr#(m2, apebs; avhdr0; isbad, err0)⟩ (avhdr = avhdr0 ∧ (bitflips ↔ isbad) ∧ err = err0)), subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE) = emptypage

Rule argument

spec: encoding-page-size-nonempty, inst: encoding-vidheader name: decode-contract seq: EB_PAGE_SIZE ≤ # buf ⊦ ⟪decode_vidheader#(EB_PAGE_SIZE, buf; vhdr; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → is-encoded(vhdr, subarray(buf, 0, EB_PAGE_SIZE)))) subst: [buf, vhdr, err] → [subarray(buf1, EB_PAGE_SIZE, EB_PAGE_SIZE), vhdr, err] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s)