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Proof step 13 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 ⊦

User applied rule apply induction

And obtained the following new goals

Proof step 12:
〈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) ∧ some(t3) ≠ some(t2)

Rule argument

[substlist-arg: [n0, t, tn1, tn0] → [m, t0, some(t2), some(t3)]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (m, t0, some(t2), some(t3))]]