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Proof step 6 from proof lebs-write-below (previous step)

n0 < n, n + m0 < # avol, n + m0 < # avol[n0, aleb], ∀ n0, n, avol, aleb. n0 < n ∧ 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 7:
n0 < n, n + m0 < # avol, ∀ n0, n, avol, aleb. n0 < n ∧ 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: append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ buf + buf0 = buf1 + buf0 ↔ buf = buf1; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)%m ≠ n ⊦ avol[m, aleb][n] = avol[n]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ # avol[n, aleb] = # avol; (s)