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Proof step 12 from proof lebs-size-mappedfull (previous step)

# lebs(avol, n, m0) = m0 * LEB_SIZE, n + m0 + 1 < # avol, n + m0 < # avol, ∀ n0. n ≤ n0 ∧ ¬ n + m0 < n0 ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE ⊦ #(lebs(avol, n, m0) + (avol[n + m0].mapped? ⊃ avol[n + m0].data + mkempbuf(LEB_SIZE - # avol[n + m0].data);mkempbuf(LEB_SIZE))) = LEB_SIZE * m0 + LEB_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# lebs(avol, n, m0) = m0 * LEB_SIZE, n + m0 + 1 < # avol, n + m0 < # avol, ∀ n0. n ≤ n0 ∧ ¬ n + m0 < n0 ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE ⊦ # (avol[n + m0].mapped? ⊃ avol[n + m0].data + mkempbuf(LEB_SIZE - # avol[n + m0].data);mkempbuf(LEB_SIZE)) = LEB_SIZE

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)