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Proof step 24 from proof lebs-range-eq (previous step)

lebs(avol0, n0, n) = lebs(avol1, n0, n), n0 + n < m + m2, n0 + n < # avol1, n0 + n < # avol0, m + m2 ≤ # avol1, m + m2 ≤ # avol0, m ≤ n0, (n0 - m) + n < m2 → avol0[n + n0] = avol1[n + n0] ⊦ (avol0[n0 + n].mapped? ⊃ avol0[n0 + n].data + mkempbuf(LEB_SIZE - # avol0[n0 + n].data);mkempbuf(LEB_SIZE)) = (avol1[n0 + n].mapped? ⊃ avol1[n0 + n].data + mkempbuf(LEB_SIZE - # avol1[n0 + n].data);mkempbuf(LEB_SIZE))

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n0, m, n1]

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n0, m, n1