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Proof step 95 from proof ks-RED (previous step)

〈RED1(ks(n1 + 2); tn)〉 tn = some(ks(n1)), ∀ n0. n0 < n1 + 2 → (true → 〈RED(ks(n0); t)〉 ((even(n0) → t = K) ∧ (odd(n0) → t = K _ K))) ⊦ 〈RED(ks(n1); t0)〉 ((even(n1) → t0 = K) ∧ (odd(n1) → t0 = K _ K))

User applied rule apply induction

And obtained the following new goals

Proof step 94:
〈RED(ks(n1); t)〉 ((even(n1) → t = K) ∧ (odd(n1) → t = K _ K)), 〈RED1(ks(n1 + 2); tn)〉 tn = some(ks(n1)), ∀ n0. n0 < n1 + 2 → (true → 〈RED(ks(n0); t)〉 ((even(n0) → t = K) ∧ (odd(n0) → t = K _ K))) ⊦ 〈RED(ks(n1); t0)〉 ((even(n1) → t0 = K) ∧ (odd(n1) → t0 = K _ K))

Rule argument

[substlist-arg: [n0] → [n1]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ m + m0 ≤ m ↔ m0 = 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (n1)]]