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Proof step 16 from proof challenge3a (previous step)

0 = # ar1 - n, m2 = m0, ar[m] = ar[n0], ¬ bv0, ar1 = ar, m ≠ n0, n0 < # ar, m < # ar, m0 < # ar, ∀ m1. m1 < m0 → (∀ n. m1 < n ∧ n < # ar → ar[m1] ≠ ar[n]), m2 < n, n ≤ # ar1, ∀ n0. m2 < n0 ∧ n0 < n → ar1[n0] ≠ ar1[m2] ⊦ ⦉while n < # ar1 ∧ ¬ bv0 do if ar1[m2] = ar1[n] then m1 := m2, n2 := n, bv0 := true else n := n + 1⦊ ⦉m2 := m2 + 1⦊ ( (bv0 ⊃ (ar[m1] = ar[n2] ∧ m1 ≠ n2 ∧ m1 < # ar ∧ n2 < # ar); (∀ m1. m1 < m2 → (∀ n. m1 < n ∧ n < # ar → ar[m1] ≠ ar[n]))) ∧ m2 ≤ # ar ∧ (∃ m, n. ar1[m] = ar1[n] ∧ m ≠ n ∧ m < # ar1 ∧ n < # ar1) ∧ ¬ m2 ≤ m0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
m2 = m0, # ar = n, ¬ bv0, ar1 = ar, ar[m] = ar[n0], m ≠ n0, m0 < # ar, m < # ar, n0 < # ar, ∀ n0. m0 < n0 ∧ n0 < # ar → ar[n0] ≠ ar[m0], ∀ m1. m1 < m0 → (∀ n. m1 < n ∧ n < # ar → ar[m1] ≠ ar[n]) ⊦ ⦉while n < # ar1 ∧ ¬ bv0 do if ar1[m2] = ar1[n] then m1 := m2, n2 := n, bv0 := true else n := n + 1⦊ ⦉m2 := m2 + 1⦊ ( (bv0 ⊃ (ar[m1] = ar[n2] ∧ m1 ≠ n2 ∧ m1 < # ar ∧ n2 < # ar); (∀ m1. m1 < m2 → (∀ n. m1 < n ∧ n < # ar → ar[m1] ≠ ar[n]))) ∧ m2 ≤ # ar ∧ (∃ m, n. ar1[m] = ar1[n] ∧ m ≠ n ∧ m < # ar1 ∧ n < # ar1) ∧ ¬ m2 ≤ m0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m ≤ m], [CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n ∧ n = n0 → m < n0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n ∧ m = n0 → n0 < n], [CSIMPFORWARD : ⊦ m < n ∧ n ≤ n0 → m < n0], [CSIMPSEQ : ⊦ m ≤ n → (n - m = 0 ↔ n = m)])]]