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Proof step 19 from proof inv-read-vidhdr (previous step)

pebs[m0] = mkpeb(buf0, m1, false), subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE) ≠ emptypage, m0 < # pebs, mtd-cons(pebs), 2 * EB_PAGE_SIZE ≤ PEB_SIZE ⊦ ⟪decode_vidheader#(EB_PAGE_SIZE, subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE); vhdr; err); if err = ESUCCESS then avhdr := avidhdr(vhdr.vol, vhdr.leb, vhdr.sqn, vhdr.size, vhdr.checksum)⟫ true

User applied rule insert program lemma

And obtained the following new goals

Proof step 20:
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 21:
pebs[m0] = mkpeb(buf0, m1, false), buf1 = subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE), m0 < # pebs, mtd-cons(pebs), 2 * EB_PAGE_SIZE ≤ PEB_SIZE, EB_PAGE_SIZE ≤ # subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE) ⊦ [decode_vidheader#(EB_PAGE_SIZE, subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE); vhdr; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded(vhdr, subarray(buf1, 0, EB_PAGE_SIZE))) → ⟪if err = ESUCCESS then avhdr := avidhdr(vhdr.vol, vhdr.leb, vhdr.sqn, vhdr.size, vhdr.checksum)⟫ true), subarray(buf0, 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(buf0, 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)