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Proof step 42 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) < 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 ⊦ # avol = 0, sb = sb0, # buf0 ≤ # buf3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# 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

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)