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Proof step 11 from proof subst-SS-equal (previous step)

S _ v4 = C0[S _ v1 _ v2 _ v3], context(C0), value(v4), value(t0), value(t), value(v1), value(v2), value(v3) ⊦ v4 _ t _ (t0 _ t) = C0[v1 _ v3 _ (v2 _ v3)] _ t0 _ t

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
⊦ O[t] = t
Proof step 7:
⊦ (C _ t1)[t] = C[t] _ t1
Proof step 8:
⊦ C[t _ t0] ≠ S
Proof step 9:
⊦ (t1 _ C)[t] = t1 _ C[t]
Proof step 10:
⊦ ¬ value(C[S _ t _ t0 _ t1])

Rule argument

[var-arg: C0]

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)])]]