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Proof step 116 from proof kappa-RED1 (previous step)

〈TOPRED(t0 _ t1; tn)〉 tn = none, 〈RED1(t1; tn4): m 〉 tn4 = none, 〈RED1(t0; tn3): m 〉 tn3 = none, 〈TOPRED(t0 _ t1; tn2): m 〉 tn2 = none, 〈RED1(t0; tn5)〉 tn5 = tn6, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn6 ≠ none, value(t0) ⊦

User applied rule apply induction

And obtained the following new goals

Proof step 115:
〈TOPRED(t0 _ t1; tn)〉 tn = none, 〈RED1(t1; tn4): m 〉 tn4 = none, 〈RED1(t0; tn3): m 〉 tn3 = none, 〈TOPRED(t0 _ t1; tn2): m 〉 tn2 = none, 〈RED1(t0; tn5)〉 tn5 = tn6, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn6 ≠ none, value(t0) ⊦ 〈RED1(t0; tn2): m 〉 tn2 = none ∧ 〈RED1(t0; tn2)〉 tn2 = tn6 ∧ tn6 ≠ none

Rule argument

[substlist-arg: [n0, t, tn1, tn0] → [m, t0, none, tn6]]

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, none, tn6)]]