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Proof step 595 from proof SII-loops (previous step)

〈RED1(t4; tn0): (2 + m0) -1 〉〈if tn0 ≠ none then RED(tn0 .t; t3): (2 + m0) -1 else t3 := t4〉 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, t3 = t1 ∧ t4 = 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))), tn0 = none ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 594:
〈RED1(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))); tn0): 1 + m0 〉〈if tn0 ≠ none then RED(tn0 .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 ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n ≤ m → m + n0 - n = (m - n) + n0], [CSIMPSEQ : ⊦ n -1 = n - 1])]]