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Proof step 37 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 + buf2, 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, 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, # buf3 ≤ encoding-size(sb, EB_PAGE_SIZE) ∧ encoding-size(sb, EB_PAGE_SIZE) ≤ # buf3 + # buf2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# 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

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ m < n → m ≤ n; (s)