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Proof step 10 from proof mapped-full-range-eq (previous step)

# buf = LEB_SIZE, avol1[n] = mapped(buf), avol0[m + (n - m)] = avol1[m + (n - m)], m < # avol1, m < n0 + n1, n0 < # avol0, n < m + m2, n < n0 + n1, m < # avol0, n0 < m + m2, n < # avol1, n < # avol0, n0 < # avol1, m + m2 ≤ # avol1, m + m2 ≤ # avol0, m ≤ n0, n0 + n1 ≤ m + m2, n0 ≤ n, m ≤ n, n0 + n1 ≤ # avol1, n0 + n1 ≤ # avol0 ⊦ m2 = 0, n1 = 0, avol0[n].mapped? ∧ # avol0[n].data = 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] → [n, m, n2]

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)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, m, n2