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Proof step 16 from proof irred-top-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
value(v3), value(v2), value(v1), ∀ t'. ¬ S _ v1 _ v2 => t' ⊦ value(S _ v1 _ v2), ∃ v. S _ v1 _ v2 _ v3 = K _ (v1 _ v3 _ (v2 _ v3)) _ v ∧ value(v1 _ v3 _ (v2 _ v3)) ∧ value(v), ∃ v, v0, v4. S _ v1 _ v2 _ v3 = S _ v _ v0 _ v4 ∧ v1 _ v3 _ (v2 _ v3) = v _ v4 _ (v0 _ v4) ∧ value(v) ∧ value(v0) ∧ value(v4)

Rule argument

[emptyarg]

Additional information

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