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Proof step 32 from proof irred-top (previous step)

∀ t'. ¬ t1 => t', value(t1), ∀ t'. ¬ t2 => t', t1 _ t2 => t' ⊦ (∃ v1, v2. t1 _ t2 = K _ v1 _ v2 ∧ t' = v1 ∧ value(v1) ∧ value(v2)) ∨ (∃ v1, v2, v3. t1 _ t2 = S _ v1 _ v2 _ v3 ∧ t' = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
value(t1), t1 _ t2 => t', ∀ t'. ¬ t1 => t', ∀ t'. ¬ t2 => t' ⊦ ∃ v1, v2, v3. t1 _ t2 = S _ v1 _ v2 _ v3 ∧ t' = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3), ∃ v2. t1 _ t2 = K _ t' _ v2 ∧ value(t') ∧ value(v2)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]