[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 43 from proof challenge3b (previous step)

m2 < # ar1 ∧ ¬ bv0, bv0 ⊃ (ar1[m1] = ar1[n2] ∧ ar[m1] ≠ a1 ∧ m1 ≠ n2 ∧ m1 < # ar1 ∧ n2 < # ar1) ; (∀ m1. m1 < m2 → (∀ n. m1 < n ∧ n < # ar1 → ar1[m1] ≠ ar1[n] ∨ ar[m1] = a1)), m2 ≤ # ar1, ar1 = ar, a1 = a, ∃ m, n. ar1[m] = ar1[n] ∧ ar[m] ≠ a1 ∧ m ≠ n ∧ m < # ar1 ∧ n < # ar1, m2 = m0, n = m2 + 1 ⊦ ⦉while n < # ar1 ∧ ¬ bv0 do if ar1[m2] = ar1[n] ∧ ar1[m2] ≠ a1 then m1 := m2, n2 := n, bv0 := true else n := n + 1⦊ ⦉m2 := m2 + 1⦊ ( (bv0 ⊃ (ar1[m1] = ar1[n2] ∧ ar[m1] ≠ a1 ∧ m1 ≠ n2 ∧ m1 < # ar1 ∧ n2 < # ar1) ; (∀ m1. m1 < m2 → (∀ n. m1 < n ∧ n < # ar1 → ar1[m1] ≠ ar1[n] ∨ ar[m1] = a1)) ) ∧ m2 ≤ # ar1 ∧ ar1 = ar ∧ a1 = a ∧ (∃ m, n. ar1[m] = ar1[n] ∧ ar[m] ≠ a1 ∧ m ≠ n ∧ m < # ar1 ∧ n < # ar1) ∧ # ar - m2 < # ar - m0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
m2 = m0, n = m0 + 1, ar[m] = ar[n0], ¬ bv0, ar1 = ar, a1 = a, ar[n0] ≠ a, m ≠ n0, n0 < # ar, m < # ar, m0 < # ar, ∀ m1. m1 < m0 → (∀ n. m1 < n ∧ n < # ar → ar[m1] ≠ ar[n] ∨ ar[m1] = a) ⊦ ⦉while n < # ar1 ∧ ¬ bv0 do if ar1[m2] = ar1[n] ∧ ar1[m2] ≠ a1 then m1 := m2, n2 := n, bv0 := true else n := n + 1⦊ ⦉m2 := m2 + 1⦊ ( (bv0 ⊃ (ar[m1] = ar[n2] ∧ ar[m1] ≠ a ∧ m1 ≠ n2 ∧ m1 < # ar ∧ n2 < # ar) ; (∀ m1. m1 < m2 → (∀ n. m1 < n ∧ n < # ar → ar[m1] ≠ ar[n] ∨ ar[m1] = a)) ) ∧ m2 ≤ # ar ∧ (∃ m, n. ar1[m] = ar1[n] ∧ ar[m] ≠ a1 ∧ m ≠ n ∧ m < # ar1 ∧ n < # ar1) ∧ ¬ m2 ≤ m0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + 1 ≤ n ↔ m < n], [CSIMPFORWARD : ⊦ m < n ∧ m = n0 → n0 < n], [CSIMPFORWARD : ⊦ m = n + 1 ∧ n < n0 → m ≤ n0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n ≤ m + n0 ↔ n ≤ n0], [CSIMPSEQ : n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m ≤ n → (n < m ↔ false)], [CSIMPSEQ : ⊦ m < n → m ≤ n])]]