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Proof step 629 from proof SII-loops (previous step)

〈TOPRED(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))); tn1): m 〉〈if tn1 = none then { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m ; 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, m0 = m + 1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 628:
〈TOPRED(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))); tn1): m 〉〈if tn1 = none then { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m ; 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): 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) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + 1 ≠ 0])]]