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Proof step 529 from proof SII-loops (previous step)

〈RED1(S _ (S _ K _ K); tn): m0 〉〈if tn ≠ none then tn := some(tn .t _ (S _ K _ K)) else { RED1(S _ K _ K; tn): m0 ; if tn ≠ none then tn := some(S _ (S _ K _ K) _ tn .t) }〉〈tn0 := tn ; if tn0 ≠ none then tn0 := some(tn0 .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn0): m ; if tn0 ≠ none then tn0 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn0 .t) }〉〈if tn0 ≠ none then RED(tn0 .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, m0 ≠ 0, m = m0 + 1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 528:
〈RED1(S _ (S _ K _ K); tn): m0 〉〈if tn ≠ none then tn := some(tn .t _ (S _ K _ K)) else { RED1(S _ K _ K; tn): m0 ; if tn ≠ none then tn := some(S _ (S _ K _ K) _ tn .t) }〉〈tn0 := tn ; m := m0 + 1 ; if tn0 ≠ none then tn0 := some(tn0 .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn0): m ; if tn0 ≠ none then tn0 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn0 .t) }〉〈if tn0 ≠ none then RED(tn0 .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 < (((((m0 + 1) + 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), m0 ≠ 0 ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + 1 ≠ 0])]]