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Proof step 34 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) + mkempbuf(n0), 0, encoding-size(sb, EB_PAGE_SIZE)) = buf0 + buf, ebm-vol-inv(avol), is-encoded-unaligned(sb, buf0), is-encoded-unaligned(sb0, buf3), encoding-size(sb, EB_PAGE_SIZE) ≤ LEB_SIZE, encoding-size(sb0, EB_PAGE_SIZE) ≤ LEB_SIZE ⊦ # avol = 0, sb = sb0, #(buf3 + buf2) ≤ encoding-size(sb, EB_PAGE_SIZE) ∧ encoding-size(sb, EB_PAGE_SIZE) ≤ #(buf3 + buf2) + # mkempbuf(n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
# 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) < 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: ⊦ LEB_SIZE ≠ 0; (s)% ⊦ m < n → m ≤ n; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ m < n → ¬ n < m; (s)% ⊦ m < n → n ≠ 0; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n + 0 = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ # mkempbuf(n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)