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Proof step 28 from proof irred-top-01 (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 14:
t1 _ t2 = C[K _ v _ v0] ∧ t' = C[v] ∧ value(v) ∧ value(v0) ∧ context(C), ∀ t'. ¬ t1 => t' ⊦ value(t1), ∃ 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)
Proof step 27:
t1 _ t2 = C[S _ v1 _ v2 _ v3] ∧ t' = C[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(C), ∀ t'. ¬ t1 => t' ⊦ value(t1), ∃ 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

[CASEDARG : pos: left 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]