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Proof step 7 from proof mapped-full-idexpt-below (previous step)

# avol1 = # avol0, n < m0, ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m], ∀ n0. m0 ≤ n0 ∧ n0 < m0 + m1 ∧ n0 < # avol0 → avol1[n0].mapped? ∧ # avol1[n0].data = LEB_SIZE ⊦ ∀ n0. m0 ≤ n0 ∧ n0 < m0 + m1 ∧ n0 < # avol0 → avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# avol1 = # avol0, n + 1 < m0 + m1, n + 1 < # avol0, n < m0, n0 < m0 + m1, n < n0, n0 < # avol0, m0 < # avol0, n < m0 + m1, n < # avol0, m0 ≤ n0, ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m], ∀ n0. m0 ≤ n0 ∧ n0 < m0 + m1 ∧ n0 < # avol0 → avol1[n0].mapped? ∧ # avol1[n0].data = LEB_SIZE ⊦ m1 = 0, avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat