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Proof step 554 from proof SII-loops (previous step)

〈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))) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 553:
〈TOPRED(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 _ (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)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ 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 ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ap(t _ t0)], [CSIMPSEQ : ⊦ value (S _ (S _ K _ K) _ (S _ K _ K))], [CSIMPSEQ : ⊦ (t _ t0) .2 = t0], [CSIMPSEQ : ⊦ (t _ t0) .1 = t], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ (m + 1) -1 = m])]]