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Proof step 38 from proof prepost-read-superblock (previous step)

# buf3 + # buf2 = encoding-size(sb0, EB_PAGE_SIZE), LEB_SIZE = n0 + encoding-size(sb0, EB_PAGE_SIZE), avol[0] = mapped(buf3 + buf2), subarray(buf3, 0, encoding-size(sb, EB_PAGE_SIZE)) = buf0 + buf, encoding-size(sb, EB_PAGE_SIZE) < # buf3, encoding-size(sb, EB_PAGE_SIZE) < LEB_SIZE, encoding-size(sb, EB_PAGE_SIZE) < encoding-size(sb0, EB_PAGE_SIZE), ebm-vol-inv(avol), is-encoded-unaligned(sb, buf0), is-encoded-unaligned(sb0, buf3), encoding-size(sb0, EB_PAGE_SIZE) ≤ LEB_SIZE ⊦ # avol = 0, sb = sb0

User applied rule apply lemma

And obtained the following new goals

Proof step 39:
⊦ is-encoded-unaligned(sb, buf) ∧ n ≤ # buf → (is-encoded-unaligned(sb0, subarray(buf, 0, n)) ↔ sb0 = sb ∧ n = # buf)
Proof step 40:
# buf3 + # buf2 = encoding-size(sb0, EB_PAGE_SIZE), LEB_SIZE = n0 + encoding-size(sb0, EB_PAGE_SIZE), avol[0] = mapped(buf3 + buf2), subarray(buf3, 0, encoding-size(sb, EB_PAGE_SIZE)) = buf0 + buf, encoding-size(sb, EB_PAGE_SIZE) < encoding-size(sb0, EB_PAGE_SIZE), encoding-size(sb, EB_PAGE_SIZE) < LEB_SIZE, encoding-size(sb, EB_PAGE_SIZE) < # buf3, ebm-vol-inv(avol), is-encoded-unaligned(sb0, buf3), is-encoded-unaligned(sb, buf0), encoding-size(sb0, EB_PAGE_SIZE) ≤ LEB_SIZE, is-encoded-unaligned(sb0, buf3) ∧ # buf0 ≤ # buf3 → (is-encoded-unaligned(sb, subarray(buf3, 0, # buf0)) ↔ sb = sb0 ∧ # buf0 = # buf3) ⊦ # avol = 0, sb = sb0

Rule argument

spec: encoding, inst: encoding-superblock name: is-encoded-unique-size seq: ⊦ is-encoded-unaligned(sb, buf) ∧ n ≤ # buf → ( is-encoded-unaligned(sb0, subarray(buf, 0, n)) ↔ sb0 = sb ∧ n = # buf) subst: [sb, buf, n, sb0] → [sb0, buf3, # buf0, sb]

Additional information

Used terms: sb0, buf3, # buf0, sb