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Proof step 46 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, is-encoded-unaligned(sb, subarray(buf3, 0, # buf0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
n + m ≤ # buf, n0 = # buf ⊦ subarray(buf, n, m) = buf0 ↔ (∃ buf1, buf2. buf = buf1 + buf0 + buf2 ∧ # buf1 = n ∧ # buf2 = n0 - n + m)

Rule argument

spec: array-splice, inst: buffer name: subarray-eq-elim seq: n + m ≤ # buf, n0 = # buf ⊦ subarray(buf, n, m) = buf0 ↔ (∃ buf1, buf2. buf = buf1 + buf0 + buf2 ∧ # buf1 = n ∧ # buf2 = n0 - n + m) subst: [n0, buf0, m, n, buf] → [# buf3, buf0 + buf, encoding-size(sb, EB_PAGE_SIZE), 0, buf3] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # buf = 0 → buf + buf0 = buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → m ≤ n; (s)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%⊦ is-encoded-unaligned(sb, buf) → (is-encoded-unaligned(sb0, buf) ↔ sb = sb0); (s) Used terms: # buf3, buf0 + buf, encoding-size(sb, EB_PAGE_SIZE), 0, buf3