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Proof step 7 from proof mapped-full-range-eq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# buf = LEB_SIZE, avol1[n] = mapped(buf), 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, ∀ n. n < m2 → avol0[m + n] = avol1[m + n] ⊦ m2 = 0, n1 = 0, avol0[n].mapped? ∧ # avol0[n].data = LEB_SIZE

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)% ⊦ mapped(buf).data = buf; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat