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Proof step 645 from proof SII-loops (previous step)

〈let v1 = S _ K _ K, v2 = S _ K _ K, v3 = S _ (S _ K _ K) _ (S _ K _ K) 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): m0 ; 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): m0 ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) } }〉〈if tn1 ≠ none then RED(tn1 .t; t3): m0 + 1 else t3 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉 t3 = 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 ⊦

Heuristic symbolic execution applied rule vardecls left

And obtained the following new goals

Proof step 644:
〈if value(v4) ∧ value(v0) ∧ value(v) then tn0 := some(v4 _ v _ (v0 _ v)) else tn0 := none〉〈tn1 := tn0 ; if tn1 = none then { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m0 ; 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): m0 ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) } }〉〈if tn1 ≠ none then RED(tn1 .t; t3): m0 + 1 else t3 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉 t3 = 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, v = S _ (S _ K _ K) _ (S _ K _ K), v0 = S _ K _ K, v4 = S _ K _ K ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]