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Proof step 13 from proof irred-top (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
context(C0), value(v0), value(v), value(v4), ∀ t'. ¬ C0[K _ v _ v0] => t', ∀ t'. ¬ v4 => t' ⊦ ∃ v1. v4 _ C0[K _ v _ v0] = K _ (v4 _ C0[v]) _ v1 ∧ value(v4 _ C0[v]) ∧ value(v1), ∃ v1, v2, v3. v4 _ C0[K _ v _ v0] = S _ v1 _ v2 _ v3 ∧ v4 _ C0[v] = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ context(t _ C) ↔ ¬ ¬ (context(C) ∧ value(t))], [CSIMPSEQ : ⊦ t _ t0 = t1 _ t2 ↔ t = t1 ∧ t0 = t2], [CSIMPSEQ : ⊦ (t1 _ C)[t] = t1 _ C[t]])]]