[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 619 from proof SII-loops (previous step)

〈tn0 := tn, t0 := S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))〉〈if m = 0 then abort else { TOPRED(t0; tn0): m -1 ; if tn0 = none ∧ ap(t0) then { RED1(t0 .1; tn0): m -1 ; if tn0 ≠ none then tn0 := some(tn0 .t _ t0 .2) else if value(t0 .1) then { RED1(t0 .2; tn0): m -1 ; if tn0 ≠ none then tn0 := some(t0 .1 _ tn0 .t) } } }〉〈tn := tn0 ; if tn ≠ none then tn := some(tn .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))))〉〈if tn ≠ none then RED(tn .t; t1): m + 1 else t1 := S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t1 = t, ∀ kappa0, t. kappa0 < ((m + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false), m ≠ 0 ⊦

Heuristic symbolic execution applied rule assign left

And obtained the following new goals

Proof step 618:
〈if m = 0 then abort else { TOPRED(t2; tn1): m -1 ; if tn1 = none ∧ ap(t2) then { RED1(t2 .1; tn1): m -1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ t2 .2) else if value(t2 .1) then { RED1(t2 .2; tn1): m -1 ; if tn1 ≠ none then tn1 := some(t2 .1 _ tn1 .t) } } }〉〈tn := tn1 ; if tn ≠ none then tn := some(tn .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))))〉〈if tn ≠ none then RED(tn .t; t1): m + 1 else t1 := S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t1 = t, ∀ kappa0, t. kappa0 < ((m + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false), m ≠ 0, tn1 = tn ∧ t2 = S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]