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Proof step 549 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(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, tn0 = tn1 ∧ t1 = S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))) ⊦

Heuristic symbolic execution applied rule if positive left

And obtained the following new goals

Proof step 548:
〈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〉〈tn1 := tn0 ; 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, tn0 = tn1 ∧ t1 = S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))) ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

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