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Proof step 22 from proof reduce-unique (previous step)

C[t3] = C0[S _ v1 _ v2 _ v3], value(v1), value(v2), value(v3), context(C0), context(C), t3 = K _ v _ v0 ∧ t0 = v ∧ value(v) ∧ value(v0) ∨ t3 = S _ v4 _ v5 _ v6 ∧ t0 = v4 _ v6 _ (v5 _ v6) ∧ value(v4) ∧ value(v5) ∧ value(v6) ⊦ C[t0] = C0[v1 _ v3 _ (v2 _ v3)]

User applied rule case distinction

And obtained the following new goals

Proof step 18:
t3 = K _ v _ v0 ∧ t0 = v ∧ value(v) ∧ value(v0), C[t3] = C0[S _ v1 _ v2 _ v3], value(v1), value(v2), value(v3), context(C0), context(C) ⊦ C[t0] = C0[v1 _ v3 _ (v2 _ v3)]
Proof step 21:
t3 = S _ v4 _ v5 _ v6 ∧ t0 = v4 _ v6 _ (v5 _ v6) ∧ value(v4) ∧ value(v5) ∧ value(v6), C[t3] = C0[S _ v1 _ v2 _ v3], value(v1), value(v2), value(v3), context(C0), context(C) ⊦ C[t0] = C0[v1 _ v3 _ (v2 _ v3)]

Rule argument

[CASEDARG : pos: left 7, ()]

Additional information

[[CONCRETESIMPRULES : ()]]