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

pebs[m0] = mkpeb(buf0, m1, false), subarray(buf0, 0, EB_PAGE_SIZE) ≠ emptypage, m0 < # pebs, mtd-cons(pebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ ⟪decode_echeader#(EB_PAGE_SIZE, subarray(buf0, 0, EB_PAGE_SIZE); ehdr; err); if err = ESUCCESS then aehdr := aechdr(ehdr.ec)⟫ true

User applied rule insert program lemma

And obtained the following new goals

Proof step 20:
EB_PAGE_SIZE ≤ # buf ⊦ ⟪decode_echeader#(EB_PAGE_SIZE, buf; ehdr; err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded(ehdr, subarray(buf, 0, EB_PAGE_SIZE))))
Proof step 21:
pebs[m0] = mkpeb(buf0, m1, false), buf1 = subarray(buf0, 0, EB_PAGE_SIZE), m0 < # pebs, mtd-cons(pebs), EB_PAGE_SIZE ≤ PEB_SIZE, EB_PAGE_SIZE ≤ # subarray(buf0, 0, EB_PAGE_SIZE) ⊦ [decode_echeader#(EB_PAGE_SIZE, subarray(buf0, 0, EB_PAGE_SIZE); ehdr; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded(ehdr, subarray(buf1, 0, EB_PAGE_SIZE))) → ⟪if err = ESUCCESS then aehdr := aechdr(ehdr.ec)⟫ true), subarray(buf0, 0, EB_PAGE_SIZE) = emptypage

Rule argument

spec: encoding-page-size-nonempty, inst: encoding-echeader name: decode-contract seq: EB_PAGE_SIZE ≤ # buf ⊦ ⟪decode_echeader#(EB_PAGE_SIZE, buf; ehdr; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → is-encoded(ehdr, subarray(buf, 0, EB_PAGE_SIZE)))) subst: [buf, ehdr, err] → [subarray(buf0, 0, EB_PAGE_SIZE), ehdr, err] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # pebs ⊦ pebs[n] = mkpeb(buf, m, boolvar) ∧ mtd-cons(pebs) → # buf = PEB_SIZE; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)