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Proof step 653 from proof SII-loops (previous step)

〈if m = 0 then abort else { TOPRED(t1; tn1): m -1 ; if tn1 = none ∧ ap(t1) then { RED1(t1 .1; tn1): m -1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ t1 .2) else if value(t1 .1) then { RED1(t1 .2; tn1): m -1 ; if tn1 ≠ none then tn1 := some(t1 .1 _ tn1 .t) } } }〉〈if tn1 ≠ none then RED(tn1 .t; t3): m else t3 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉 t3 = t, ∀ kappa0, t. kappa0 < m + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false), tn1 = tn0 ∧ t1 = S _ (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 652:
〈if m = 0 then abort else { TOPRED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m - 1 ; if tn1 = none then { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m - 1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ (S _ K _ K) _ (S _ K _ K))) else { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m - 1 ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) } } }〉〈if tn1 ≠ none then RED(tn1 .t; t3): m else t3 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉 t3 = t, ∀ kappa0, t. kappa0 < m + 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 : ⊦ ap(t _ t0)], [CSIMPSEQ : ⊦ value (S _ (S _ K _ K) _ (S _ K _ K))], [CSIMPSEQ : ⊦ (t _ t0) .2 = t0], [CSIMPSEQ : ⊦ (t _ t0) .1 = t], [CSIMPSEQ : ⊦ n -1 = n - 1])]]