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Proof step 11 from proof kappa-RED1 (previous step)

〈TOPRED(t0 _ t1; tn)〉 tn = none, 〈RED1(t0; tn3): m 〉 tn3 = some(t2), 〈TOPRED(t0 _ t1; tn2): m 〉 tn2 = none, 〈RED1(t0; tn4)〉 tn4 = some(t3), ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), t3 _ t1 ≠ t2 _ t1 ⊦ 〈RED1(t0; tn2): m 〉 tn2 = some(t2) ∧ 〈RED1(t0; tn2)〉 tn2 = some(t3)

Heuristic dl case distinction applied rule case distinction

And obtained the following new goals

Proof step 9:
〈RED1(t0; tn3): m 〉 tn3 = some(t2), 〈TOPRED(t0 _ t1; tn)〉 tn = none, 〈TOPRED(t0 _ t1; tn2): m 〉 tn2 = none, 〈RED1(t0; tn4)〉 tn4 = some(t3), ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), t3 _ t1 ≠ t2 _ t1 ⊦ 〈RED1(t0; tn2): m 〉 tn2 = some(t2)
Proof step 10:
〈RED1(t0; tn3): m 〉 tn3 = some(t2), 〈TOPRED(t0 _ t1; tn)〉 tn = none, 〈TOPRED(t0 _ t1; tn2): m 〉 tn2 = none, 〈RED1(t0; tn4)〉 tn4 = some(t3), ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), t3 _ t1 ≠ t2 _ t1 ⊦ 〈RED1(t0; tn2)〉 tn2 = some(t3)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]