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Proof step 17 from proof RED-complete (previous step)

〈RED1(t; tn)〉 tn = some(t2), ∀ n0, t', t. n0 < m + 1 → (irred(t') ∧ (=> ^ n0)(t, t') → 〈RED(t; t2)〉 t2 = t'), irred(t'), (=> ^ m)(t2, t'), t => t2 ⊦ 〈RED(t2; t1)〉 t1 = t'

User applied rule apply induction

And obtained the following new goals

Proof step 16:
〈RED(t2; t0)〉 t0 = t', 〈RED1(t; tn)〉 tn = some(t2), ∀ n0, t', t. n0 < m + 1 → (irred(t') ∧ (=> ^ n0)(t, t') → 〈RED(t; t2)〉 t2 = t'), irred(t'), (=> ^ m)(t2, t'), t => t2 ⊦ 〈RED(t2; t1)〉 t1 = t'

Rule argument

[substlist-arg: [n0, t', t] → [m, t', t2]]

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, t', t2)]]