[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 53 from proof challenge3a (previous step)

ar[m] = ar[n], m2 ≤ # ar, m < # ar, n < # ar, bv0 ⊃ (ar[m1] = ar[n2] ∧ m1 ≠ n2 ∧ m1 < # ar ∧ n2 < # ar) ; (∀ m1. m1 < m2 → (∀ n. m1 < n ∧ n < # ar → ar[m1] ≠ ar[n])), ar[m1] ≠ ar[n2] ∨ m1 = n2 ∨ ¬ m1 < # ar ∨ ¬ n2 < # ar ⊦ m = n, m2 < # ar ∧ ¬ bv0

User applied rule cut formula

And obtained the following new goals

Proof step 52:
ar[m] = ar[n], m2 ≤ # ar, m < # ar, n < # ar, bv0 ⊃ (ar[m1] = ar[n2] ∧ m1 ≠ n2 ∧ m1 < # ar ∧ n2 < # ar) ; (∀ m1. m1 < m2 → (∀ n. m1 < n ∧ n < # ar → ar[m1] ≠ ar[n])), ar[m1] ≠ ar[n2] ∨ m1 = n2 ∨ ¬ m1 < # ar ∨ ¬ n2 < # ar ⊦ bv0, m = n, m2 < # ar ∧ ¬ bv0

Rule argument

[fma-arg: bv0]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (bv0)]]