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Proof step 22 from proof subst-KK-equal (previous step)

C1[K _ v1 _ v2] = K _ v, context(C1), value(v0), value(v), value(v2), value(v1), ∀ v3, v4, C, v5, v6. C1[K _ v3 _ v4] = C[K _ v5 _ v6] ∧ value(v3) ∧ value(v4) ∧ value(v5) ∧ value(v6) ∧ context(C) → C1[v3] = C[v5] ⊦ C1[v1] _ v0 = v

User applied rule constructor cut

And obtained the following new goals

Proof step 17:
⊦ O[t] = t
Proof step 18:
⊦ (C _ t1)[t] = C[t] _ t1
Proof step 19:
⊦ C[t _ t0] ≠ K
Proof step 20:
⊦ (t1 _ C)[t] = t1 _ C[t]
Proof step 21:
⊦ ¬ value(C[K _ t _ t0])

Rule argument

[var-arg: C1]

Additional information

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