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Proof step 14 from proof irred-top (previous step)

t1 _ t2 = C[K _ v _ v0], value(v), value(v0), context(C), value(t1), ∀ t'. ¬ t1 => t', ∀ t'. ¬ t2 => t' ⊦ ∃ v1, v2, v3. t1 _ t2 = S _ v1 _ v2 _ v3 ∧ C[v] = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3), ∃ v2. t1 _ t2 = K _ C[v] _ v2 ∧ value(C[v]) ∧ value(v2)

User applied rule constructor cut

And obtained the following new goals

Proof step 13:
C = v4 _ C0, t1 _ t2 = C[K _ v _ v0], value(v), value(v0), context(C), value(t1), ∀ t'. ¬ t1 => t', ∀ t'. ¬ t2 => t' ⊦ ∃ v1, v2, v3. t1 _ t2 = S _ v1 _ v2 _ v3 ∧ C[v] = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3), ∃ v2. t1 _ t2 = K _ C[v] _ v2 ∧ value(C[v]) ∧ value(v2)

Rule argument

[var-arg: C]

Additional information

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