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Proof step 3 from proof K-reduce (previous step)

value(v0), value(v) ⊦ (∃ v1, v2. K _ O[v1] _ v0 = O[K _ v1 _ v2] ∧ v = O[v1] ∧ value(v1) ∧ value(v2) ∧ context(O)) ∨ (∃ v1, v2, v3. K _ O[v1 _ v3 _ (v2 _ v3)] _ v0 = O[S _ v1 _ v2 _ v3] ∧ v = O[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(O))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
value(v0), value(v) ⊦ ∃ v2. K _ v _ v0 = K _ v _ v2 ∧ value(v2), ∃ v1, v2, v3. K _ (v1 _ v3 _ (v2 _ v3)) _ v0 = S _ v1 _ v2 _ v3 ∧ v = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ context(O)], [CSIMPSEQ : ⊦ O[t] = t])]]