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Proof step 65 from proof inv-format (previous step)

# pebs0 = n0 + m1, # pebs1 = n0 + m1, pebs1[m1] = mkpeb(buf0, m2, false), buf = mkbuf(EB_PAGE_SIZE), n0 ≠ 0, mtd-cons(pebs0), mtd-cons(pebs1), mtd-cons(pebs1[m1, mkpeb(emptypeb, 0, false)]), ubi-io-initial(subarray(pebs1, 0, m1)) ⊦ ⟪encode_echeader#(EB_PAGE_SIZE, echdr(aechdr((err1 = ESUCCESS ∧ aehdr0.valid? ⊃ aehdr0.ec + 1;0)).ec); buf; err); pebs := pebs1[m1, mkpeb(emptypeb, 0, false)]; if err = ESUCCESS then mtd_asm_write#(m1, 0, 0, EB_PAGE_SIZE, buf; pebs; err); m1 := m1 + 1⟫ ( m1 ≤ # pebs0 ∧ # pebs0 = # pebs ∧ mtd-cons(pebs) ∧ (err = ESUCCESS → ubi-io-initial(subarray(pebs, 0, m1))) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # pebs0 < n0 + m1)

User applied rule insert program lemma

And obtained the following new goals

Proof step 66:
EB_PAGE_SIZE ≤ # buf, buf0 = buf ⊦ ⟪encode_echeader#(EB_PAGE_SIZE, ehdr; buf; err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ (err = ESUCCESS → is-encoded(ehdr, subarray(buf, 0, EB_PAGE_SIZE))))
Proof step 67:
# pebs1 = n0 + m1, # pebs0 = n0 + m1, pebs1[m1] = mkpeb(buf0, m2, false), buf = mkbuf(EB_PAGE_SIZE), buf = buf, buf1 = buf, ehdr0 = echdr(aechdr((err1 = ESUCCESS ∧ aehdr0.valid? ⊃ aehdr0.ec + 1;0)).ec), mtd-cons(pebs1[m1, mkpeb(emptypeb, 0, false)]), mtd-cons(pebs1), mtd-cons(pebs0), ubi-io-initial(subarray(pebs1, 0, m1)), EB_PAGE_SIZE ≤ # buf ⊦ [encode_echeader#(EB_PAGE_SIZE, echdr(aechdr((err1 = ESUCCESS ∧ aehdr0.valid? ⊃ aehdr0.ec + 1;0)).ec); buf; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf1 ∧ (err = ESUCCESS → is-encoded(ehdr0, subarray(buf, 0, EB_PAGE_SIZE))) → ⟪pebs := pebs1[m1, mkpeb(emptypeb, 0, false)]; if err = ESUCCESS then mtd_asm_write#(m1, 0, 0, EB_PAGE_SIZE, buf; pebs; err); m1 := m1 + 1⟫ ( m1 ≤ # pebs0 ∧ # pebs0 = # pebs ∧ mtd-cons(pebs) ∧ (err = ESUCCESS → ubi-io-initial(subarray(pebs, 0, m1))) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # pebs0 < n0 + m1)), n0 = 0

Rule argument

spec: encoding-page-size-nonempty, inst: encoding-echeader name: encode-contract seq: EB_PAGE_SIZE ≤ # buf, buf0 = buf ⊦ ⟪encode_echeader#(EB_PAGE_SIZE, ehdr; buf; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ ( err = ESUCCESS → is-encoded(ehdr, subarray(buf, 0, EB_PAGE_SIZE)))) subst: [ehdr, buf, err, buf0] → [echdr (aechdr((err1 = ESUCCESS ∧ aehdr0.valid? ⊃ aehdr0.ec + 1;0)) .ec), buf, err, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # mkbuf(n) = n; (s)% ⊦ m ≤ m; (s)