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Proof step 6 from proof fun-reduces-imp-app-reduces (previous step)

t = C[S _ v1 _ v2 _ v3] ∧ t' = C[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(C) ⊦ ∃ v4, v5. t _ t1 = C[K _ v4 _ v5] _ t1 ∧ t' _ t1 = C[v4] _ t1 ∧ value(v4) ∧ value(v5) ∧ context(C), ∃ v4, v5, v6. t _ t1 = C[S _ v4 _ v5 _ v6] _ t1 ∧ t' _ t1 = C[v4 _ v6 _ (v5 _ v6)] _ t1 ∧ value(v4) ∧ value(v5) ∧ value(v6) ∧ context(C)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
value(v1), value(v2), value(v3), context(C) ⊦ ∃ v, v0. C[S _ v1 _ v2 _ v3] _ t1 = C[K _ v _ v0] _ t1 ∧ C[v1 _ v3 _ (v2 _ v3)] _ t1 = C[v] _ t1 ∧ value(v) ∧ value(v0), ∃ v, v0, v4. C[S _ v1 _ v2 _ v3] _ t1 = C[S _ v _ v0 _ v4] _ t1 ∧ C[v1 _ v3 _ (v2 _ v3)] _ t1 = C[v _ v4 _ (v0 _ v4)] _ t1 ∧ value(v) ∧ value(v0) ∧ value(v4)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]