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Proof step 34 from proof subst-SS-equal (previous step)

C1[S _ v4 _ v5 _ v6] = S _ v1 _ v2, context(C1), value(v3), value(v2), value(v1), value(v6), value(v5), value(v4), ∀ v, v0, v7, C, v8, v9, v10. C1[S _ v _ v0 _ v7] = C[S _ v8 _ v9 _ v10] ∧ value(v) ∧ value(v0) ∧ value(v7) ∧ value(v8) ∧ value(v9) ∧ value(v10) ∧ context(C) → C1[v _ v7 _ (v0 _ v7)] = C[v8 _ v10 _ (v9 _ v10)] ⊦ C1[v4 _ v6 _ (v5 _ v6)] _ v3 = v1 _ v3 _ (v2 _ v3)

User applied rule constructor cut

And obtained the following new goals

Proof step 23:
⊦ O[t] = t
Proof step 31:
C1 = C0 _ t, C1[S _ v4 _ v5 _ v6] = S _ v1 _ v2, context(C1), value(v3), value(v2), value(v1), value(v6), value(v5), value(v4), ∀ v, v0, v7, C, v8, v9, v10. C1[S _ v _ v0 _ v7] = C[S _ v8 _ v9 _ v10] ∧ value(v) ∧ value(v0) ∧ value(v7) ∧ value(v8) ∧ value(v9) ∧ value(v10) ∧ context(C) → C1[v _ v7 _ (v0 _ v7)] = C[v8 _ v10 _ (v9 _ v10)] ⊦ C1[v4 _ v6 _ (v5 _ v6)] _ v3 = v1 _ v3 _ (v2 _ v3)
Proof step 32:
⊦ (t1 _ C)[t] = t1 _ C[t]
Proof step 33:
⊦ ¬ value(C[S _ t _ t0 _ t1])

Rule argument

[var-arg: C1]

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)])]]