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Proof step 15 from proof subst-SK-equal (previous step)

S _ v3 _ v4 = C[K _ v _ v0], context(C), value(v0), value(v), value(t), value(v4), value(v3) ⊦ v3 _ t _ (v4 _ t) = C[v] _ t

User applied rule constructor cut

And obtained the following new goals

Proof step 4:
⊦ O[t] = t
Proof step 12:
C = C0 _ t0, S _ v3 _ v4 = C[K _ v _ v0], context(C), value(v0), value(v), value(t), value(v4), value(v3) ⊦ v3 _ t _ (v4 _ t) = C[v] _ t
Proof step 13:
⊦ (t1 _ C)[t] = t1 _ C[t]
Proof step 14:
⊦ ¬ value(C[K _ t _ t0])

Rule argument

[var-arg: C]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : rawctxt generated by o, _, _;], [CSIMPSEQ : ⊦ K ≠ S], [CSIMPSEQ : ⊦ t _ t0 = t1 _ t2 ↔ t = t1 ∧ t0 = t2], [CSIMPSEQ : ⊦ context(t _ C) ↔ ¬ ¬ (context(C) ∧ value(t))], [CSIMPSEQ : ⊦ value(S _ t) ↔ value(t)])]]