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Proof step 544 from proof SII-loops (previous step)

〈if tn = none then { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn): m ; if tn ≠ none then tn := some(tn .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn): m ; if tn ≠ none then tn := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn .t) } }〉〈if tn ≠ none then RED(tn .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, tn = none ⊦

Heuristic symbolic execution applied rule if positive left

And obtained the following new goals

Proof step 543:
〈RED1(S _ (S _ K _ K) _ (S _ K _ K); tn): m 〉〈if tn ≠ none then tn := some(tn .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn): m ; if tn ≠ none then tn := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn .t) }〉〈if tn ≠ none then RED(tn .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, tn = none ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

[[CONCRETESIMPRULES : ()]]