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Proof step 19 from proof subst-SS-equal (previous step)

S _ v4 _ v5 _ v6 = C0[S _ v1 _ v2 _ v3], value(v4), value(v5), value(v6), value(v1), value(v2), value(v3), context(C0) ⊦ v4 _ v6 _ (v5 _ v6) = C0[v1 _ v3 _ (v2 _ v3)]

User applied rule constructor cut

And obtained the following new goals

Proof step 2:
⊦ O[t] = t
Proof step 16:
C0 = C _ t, S _ v4 _ v5 _ v6 = C0[S _ v1 _ v2 _ v3], value(v4), value(v5), value(v6), value(v1), value(v2), value(v3), context(C0) ⊦ v4 _ v6 _ (v5 _ v6) = C0[v1 _ v3 _ (v2 _ v3)]
Proof step 17:
⊦ (t1 _ C)[t] = t1 _ C[t]
Proof step 18:
⊦ ¬ value(C[S _ t _ t0 _ t1])

Rule argument

[var-arg: C0]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : rawctxt generated by o, _, _;], [CSIMPSEQ : ⊦ context(O)], [CSIMPSEQ : ⊦ t _ t0 = t1 _ t2 ↔ t = t1 ∧ t0 = t2], [CSIMPSEQ : ⊦ context(t _ C) ↔ ¬ ¬ (context(C) ∧ value(t))])]]