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Proof step 240 from proof kappa-RED1 (previous step)

〈RED1((S _ t4 _ t3 _ t1) .2; tn4)〉 tn4 = tn5, 〈RED1((S _ t4 _ t3 _ t1) .1; tn2)〉 tn2 = tn4, 〈TOPRED(S _ t4 _ t3 _ t1; tn)〉 tn = tn2, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn3): n0 〉 tn3 = tn1 ∧ 〈RED1(t; tn3)〉 tn3 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ some(t4 _ t1 _ (t3 _ t1)), m ≠ 0, value(t4), value(t3), value(t1), tn2 = none ∧ ap(S _ t4 _ t3 _ t1), ¬ tn4 ≠ none, value((S _ t4 _ t3 _ t1) .1), tn5 ≠ none, some((S _ t4 _ t3 _ t1) .1 _ tn5 .t) = tn0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 239:
〈TOPRED(S _ t4 _ t3 _ t1; tn)〉 tn = none, 〈RED1(t1; tn4)〉 tn4 = tn5, 〈RED1(S _ t4 _ t3; tn2)〉 tn2 = none, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn3): n0 〉 tn3 = tn1 ∧ 〈RED1(t; tn3)〉 tn3 = tn0 ∧ tn0 ≠ tn1 → false), m ≠ 0, tn5 ≠ none, S _ t4 _ t3 _ tn5 .t ≠ t4 _ t1 _ (t3 _ t1), value(t4), value(t3), value(t1), value(S _ t4 _ t3) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (t _ t0) .2 = t0], [CSIMPSEQ : ⊦ ap(t _ t0)], [CSIMPSEQ : ⊦ some(t) = some(t0) ↔ t = t0], [CSIMPSEQ : ⊦ (t _ t0) .1 = t])]]