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Proof step 15 from proof subst-SS-equal (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 4:
⊦ O[t] = t
Proof step 12:
C = C0 _ t0, S _ v4 _ v5 = C[S _ v1 _ v2 _ v3], context(C), value(v3), value(v2), value(v1), value(t), value(v5), value(v4) ⊦ v4 _ t _ (v5 _ t) = C[v1 _ v3 _ (v2 _ v3)] _ t
Proof step 13:
⊦ (t1 _ C)[t] = t1 _ C[t]
Proof step 14:
⊦ ¬ value(C[S _ t _ t0 _ t1])

Rule argument

[var-arg: C]

Additional information

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