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Proof step 631 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) } }〉〈if tn1 ≠ none then RED(tn1 .t; t1): 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 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false), m0 ≠ 0, tn1 = tn0 ∧ t1 = S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 630:
〈TOPRED(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))); tn1): m0 - 1 〉〈if tn1 = none then { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m0 - 1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) }〉〈if tn1 ≠ none then RED(tn1 .t; t1): 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 → (〈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 _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K) ))], [CSIMPSEQ : ⊦ (t _ t0) .2 = t0], [CSIMPSEQ : ⊦ (t _ t0) .1 = t], [CSIMPSEQ : ⊦ n -1 = n - 1])]]