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Proof step 43 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) < # buf0, # buf3 < # buf0, 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, encoding-size(sb, EB_PAGE_SIZE) + 1 < # buf0, ebm-vol-inv(avol), is-encoded-unaligned(sb0, buf3), is-encoded-unaligned(sb, buf0), encoding-size(sb0, EB_PAGE_SIZE) ≤ LEB_SIZE ⊦ # avol = 0, sb = sb0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [buf0 + buf, subarray(buf3, 0, encoding-size(sb, EB_PAGE_SIZE))] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set] Used terms: buf0 + buf, subarray(buf3, 0, encoding-size(sb, EB_PAGE_SIZE))