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Proof step 14 from proof count-mkbag-greater-two (previous step)

2 = 1 + count(A[m], mkbag(A, i0)), A[m1] = A[m], A[m0] = A[m], A[m] = A[i0], i0 < # A, m0 < # A, m < # A, m1 < # A, m0 ≤ i0, m ≤ i0, m1 ≤ i0, ∀ A, m, m1, m0. 2 = count(A[m], mkbag(A, i0)) ∧ A[m1] = A[m] ∧ A[m0] = A[m] ∧ m0 < # A ∧ m < # A ∧ m1 < # A ∧ m0 < i0 ∧ m < i0 ∧ m1 < i0 ∧ i0 ≤ # A → m = m1 ∨ m = m0 ∨ m0 = m1 ⊦ m = m1, m = m0, m0 = m1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
1 = count(A[i0], mkbag(A, i0)), A[m] = A[i0], A[m0] = A[i0], A[m1] = A[i0], m1 < # A, m < # A, m0 < # A, i0 < # A, m1 ≤ i0, m ≤ i0, m0 ≤ i0, ∀ A, m, m1, m0. 2 = count(A[m], mkbag(A, i0)) ∧ A[m1] = A[m] ∧ A[m0] = A[m] ∧ m0 < # A ∧ m < # A ∧ m1 < # A ∧ m0 < i0 ∧ m < i0 ∧ m1 < i0 ∧ i0 ≤ # A → m = m1 ∨ m = m0 ∨ m0 = m1 ⊦ m = m0, m = m1, m0 = m1

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%n0 < n ⊦ (* n) = m0 + (* n0) ↔ n - n0 = m0; (s)