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Proof step 15 from proof ks-RED1 (previous step)

〈RED1(ks(n0); tn)〉 tn = tn0, tn0 = none → n0 ≤ 1, tn0 ≠ none → ¬ n0 ≤ 1 ∧ tn0 = some(ks(n0 - 2)), ap(ks(n0) _ K) ∧ ap((ks(n0) _ K) .1) ∧ (ks(n0) _ K) .1 .1 = K ∧ value((ks(n0) _ K) .1 .2) ∧ value((ks(n0) _ K) .2), tn = some((ks(n0) _ K) .1 .2), ¬ (tn = none → n0 = 0) ∨ ¬ (tn ≠ none → n0 ≠ 0 ∧ tn = some(ks(n0 + 1 - 2))) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
〈RED1(ks(n0); tn)〉 tn = tn0, ks(n0) .1 = K, ks(n0) .2 ≠ ks(n0 + 1 - 2), n0 ≠ 0, ap(ks(n0)), value(ks(n0) .2), tn0 = none → n0 = 1, tn0 ≠ none → n0 ≠ 1 ∧ tn0 = some(ks(n0 - 2)) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m ≠ 0 → (m ≤ 1 ↔ m = 1)], [CSIMPSEQ : ⊦ ¬ ap(K)], [CSIMPSEQ : ⊦ ks(0) = K], [CSIMPSEQ : ⊦ some(t) = some(t0) ↔ t = t0], [CSIMPSEQ : ⊦ some(t) ≠ none], [CSIMPSEQ : ⊦ value(K)], [CSIMPSEQ : ⊦ (t _ t0) .2 = t0], [CSIMPSEQ : ⊦ ap(t _ t0)], [CSIMPSEQ : ⊦ (t _ t0) .1 = t])]]