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Proof step 283 from proof kappa-RED1 (previous step)

〈RED1(t; tn2)〉 tn2 = tn0, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ tn1, ¬ (tn1 = none ∧ ap(t)), tn3 = tn2, m ≠ 0, ¬ (ap(t) ∧ ap(t .1) ∧ t .1 .1 = K ∧ value(t .1 .2) ∧ value(t .2)), ap(t) ∧ ap(t .1) ∧ ap(t .1 .1) ∧ t .1 .1 .1 = S, v = t .2, v0 = t .1 .2, v4 = t .1 .1 .2, value(v4) ∧ value(v0) ∧ value(v), some(v4 _ v _ (v0 _ v)) = tn1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 282:
〈RED1(t; tn3)〉 tn3 = tn0, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn3): n0 〉 tn3 = tn1 ∧ 〈RED1(t; tn3)〉 tn3 = tn0 ∧ tn0 ≠ tn1 → false), t .1 .1 .1 = S, tn0 ≠ some(t .1 .1 .2 _ t .2 _ (t .1 .2 _ t .2)), m ≠ 0, t .1 .1 ≠ K, ap(t), ap(t .1), ap(t .1 .1), value(t .1 .1 .2), value(t .1 .2), value(t .2) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ some(t) ≠ none])]]