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Proof step 54 from proof kappa-RED1 (previous step)

〈RED1(t; tn2)〉 tn2 = tn0, 〈RED1(t .1; tn3): m 〉 tn3 = tn4, 〈TOPRED(t; tn2): m 〉 tn2 = none, ∀ n0, t, tn1, tn0. n0 < n → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ some(tn4 .t _ t .2), n ≠ 0, tn4 ≠ none, ap(t), n = m + 1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
〈RED1(t; tn2)〉 tn2 = tn0, 〈RED1(t .1; tn3): m 〉 tn3 = tn4, 〈TOPRED(t; tn2): m 〉 tn2 = none, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ some(tn4 .t _ t .2), tn4 ≠ none, ap(t) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + 1 ≠ 0])]]