[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 56 from proof challenge3a (previous step)

ar[m] = ar[n], m ≠ n, n < # ar, m < # ar, bv0 ↔ false, m2 = 0, n2 = n0 ∧ m1 = m0 ∧ ar1 = ar ⊦ ⦉while m2 < # ar1 ∧ ¬ bv0 do { let n1 = m2 + 1 in while n1 < # ar1 ∧ ¬ bv0 do if ar1[m2] = ar1[n1] then m1 := m2, n2 := n1, bv0 := true else n1 := n1 + 1 ; m2 := m2 + 1 }⦊ (ar[m1] = ar[n2] ∧ m1 ≠ n2 ∧ m1 < # ar ∧ n2 < # ar)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
m2 = 0, ar1 = ar, ar[m] = ar[n], ¬ bv0, m ≠ n, n < # ar, m < # ar ⊦ ⦉while m2 < # ar1 ∧ ¬ bv0 do { let n1 = m2 + 1 in while n1 < # ar1 ∧ ¬ bv0 do if ar1[m2] = ar1[n1] then m1 := m2, n2 := n1, bv0 := true else n1 := n1 + 1 ; m2 := m2 + 1 }⦊ (ar[m1] = ar[n2] ∧ m1 ≠ n2 ∧ m1 < # ar ∧ n2 < # ar)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]