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Proof step 578 from proof SII-loops (previous step)

〈TOPRED(t1; tn1): m0 -1 〉〈if tn1 = none ∧ ap(t1) then { RED1(t1 .1; tn1): m0 -1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ t1 .2) else if value(t1 .1) then { RED1(t1 .2; tn1): m0 -1 ; if tn1 ≠ none then tn1 := some(t1 .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; t3): 1 + m0 else t3 := K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (K _ (S _ (S _ K _ K) _ (S _ K _ K))) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t3 = 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), m0 ≠ 0, tn1 = tn ∧ t1 = K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (K _ (S _ (S _ K _ K) _ (S _ K _ K))) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 577:
〈TOPRED(K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (K _ (S _ (S _ K _ K) _ (S _ K _ K))); tn1): m0 - 1 〉〈if tn1 = none then { RED1(K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m0 - 1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m0 - 1 ; if tn1 ≠ none then tn1 := some(K _ (S _ (S _ K _ K) _ (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; t3): 1 + m0 else t3 := K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (K _ (S _ (S _ K _ K) _ (S _ K _ K))) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t3 = 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), m0 ≠ 0 ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ap(t _ t0)], [CSIMPSEQ : ⊦ value (S _ (S _ K _ K) _ (S _ K _ K))], [CSIMPSEQ : ⊦ value(K _ t) ↔ value(t)], [CSIMPSEQ : ⊦ (t _ t0) .2 = t0], [CSIMPSEQ : ⊦ (t _ t0) .1 = t], [CSIMPSEQ : ⊦ n -1 = n - 1])]]