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Proof step 556 from proof SII-loops (previous step)

〈tn := tn0, t0 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉〈if 1 + m = 0 then abort else { TOPRED(t0; tn): (1 + m) -1 ; if tn = none ∧ ap(t0) then { RED1(t0 .1; tn): (1 + m) -1 ; if tn ≠ none then tn := some(tn .t _ t0 .2) else if value(t0 .1) then { RED1(t0 .2; tn): (1 + m) -1 ; if tn ≠ none then tn := some(t0 .1 _ tn .t) } } }〉〈if tn ≠ none then RED(tn .t; t2): 1 + m else t2 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t2 = t, ∀ kappa0, t. kappa0 < ((((m + 1) + 1) + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t2): kappa0 〉 t2 = t → false), m ≠ 0 ⊦

Heuristic symbolic execution applied rule assign left

And obtained the following new goals

Proof step 555:
〈if 1 + m = 0 then abort else { TOPRED(t1; tn1): (1 + m) -1 ; if tn1 = none ∧ ap(t1) then { RED1(t1 .1; tn1): (1 + m) -1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ t1 .2) else if value(t1 .1) then { RED1(t1 .2; tn1): (1 + m) -1 ; if tn1 ≠ none then tn1 := some(t1 .1 _ tn1 .t) } } }〉〈if tn1 ≠ none then RED(tn1 .t; t2): 1 + m else t2 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t2 = t, ∀ kappa0, t. kappa0 < ((((m + 1) + 1) + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t2): kappa0 〉 t2 = t → false), m ≠ 0, tn1 = tn0 ∧ t1 = S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]