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Proof step 12 from proof irred-top-01 (previous step)

C = C0 _ v4, t1 _ t2 = C[K _ v _ v0], value(v), value(v0), context(C), ∀ t'. ¬ t1 => t' ⊦ value(t1), ∃ 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 11:
context(C0), value(v0), value(v), ∀ t'. ¬ C0[K _ v _ v0] => t' ⊦ ∃ v1. C0[K _ v _ v0] _ v4 = K _ (C0[v] _ v4) _ v1 ∧ value(C0[v] _ v4) ∧ value(v1), ∃ v1, v2, v3. C0[K _ v _ v0] _ v4 = S _ v1 _ v2 _ v3 ∧ C0[v] _ v4 = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3)

Rule argument

[emptyarg]

Additional information

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