[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 613 from proof SII-loops (previous step)

〈tn := tn1, t0 := S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))〉〈if m0 = 0 then abort else if ap(t0) ∧ ap(t0 .1) ∧ t0 .1 .1 = K ∧ value(t0 .1 .2) ∧ value(t0 .2) then tn := some(t0 .1 .2) else if ap(t0) ∧ ap(t0 .1) ∧ ap(t0 .1 .1) ∧ t0 .1 .1 .1 = S then let v1 = t0 .1 .1 .2, v2 = t0 .1 .2, v3 = t0 .2 in if value(v1) ∧ value(v2) ∧ value(v3) then tn := some(v1 _ v3 _ (v2 _ v3)) else tn := none else tn := none〉〈tn1 := tn ; if tn1 = none then { RED1(S _ K _ K; tn1): m0 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ (S _ K _ K) _ (S _ K _ K))) else { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m0 ; if tn1 ≠ none then tn1 := some(S _ K _ K _ 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): 2 + m0 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 < (((m0 + 1) + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false) ⊦

Heuristic symbolic execution applied rule assign left

And obtained the following new goals

Proof step 612:
〈if m0 = 0 then abort else if ap(t2) ∧ ap(t2 .1) ∧ t2 .1 .1 = K ∧ value(t2 .1 .2) ∧ value(t2 .2) then tn0 := some(t2 .1 .2) else if ap(t2) ∧ ap(t2 .1) ∧ ap(t2 .1 .1) ∧ t2 .1 .1 .1 = S then let v1 = t2 .1 .1 .2, v2 = t2 .1 .2, v3 = t2 .2 in if value(v1) ∧ value(v2) ∧ value(v3) then tn0 := some(v1 _ v3 _ (v2 _ v3)) else tn0 := none else tn0 := none〉〈tn1 := tn0 ; if tn1 = none then { RED1(S _ K _ K; tn1): m0 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ (S _ K _ K) _ (S _ K _ K))) else { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m0 ; if tn1 ≠ none then tn1 := some(S _ K _ K _ tn1 .t) } }〉〈tn0 := tn1 ; if tn0 ≠ none then tn0 := some(tn0 .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))))〉〈if tn0 ≠ none then RED(tn0 .t; t1): 2 + m0 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 < (((m0 + 1) + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false), tn0 = tn1 ∧ t2 = S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]