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Proof step 586 from proof SII-loops (previous step)

〈if ap(t1) ∧ ap(t1 .1) ∧ ap(t1 .1 .1) ∧ t1 .1 .1 .1 = S then let v1 = t1 .1 .1 .2, v2 = t1 .1 .2, v3 = t1 .2 in if value(v1) ∧ value(v2) ∧ value(v3) then tn0 := some(v1 _ v3 _ (v2 _ v3)) else tn0 := none else tn0 := none〉 〈tn1 := tn0 ; if tn1 = none then { RED1(K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (K _ (S _ (S _ K _ K) _ (S _ K _ K))); tn1): m0 ; 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; 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, tn0 = tn1 ∧ t1 = 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))) ⊦

Heuristic symbolic execution applied rule if negative left

And obtained the following new goals

Rule argument

[fmapos-arg: pos: left 1]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ap(t _ t0)], [CSIMPSEQ : ⊦ (t _ t0) .1 = t], [CSIMPSEQ : ⊦ K ≠ S])]]