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Proof step 7 from proof lebs-write-above (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
n + m0 < n0, n + m0 < # avol, ∀ n, n0, avol, aleb. n + m0 ≤ n0 ∧ n + m0 ≤ # avol → lebs(avol[n0, aleb], n, m0) = lebs(avol, n, m0) ⊦ lebs(avol[n0, aleb], n, m0) = lebs(avol, n, m0)

Rule argument

Additional information

Used simplifier rules: ⊦ # avol[n, aleb] = # avol; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ buf + buf0 = buf1 + buf0 ↔ buf = buf1; (s)% ⊦ n < m → avol[m, aleb][n] = avol[n]; (s)