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Proof step 52 from proof subst-SS-equal (previous step)

∀ v4, v5, v6, C0, v1, v2, v3. C1[S _ v4 _ v5 _ v6] = C0[S _ v1 _ v2 _ v3] ∧ value(v4) ∧ value(v5) ∧ value(v6) ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(C0) ∧ context(C1) → C1[v4 _ v6 _ (v5 _ v6)] = C0[v1 _ v3 _ (v2 _ v3)], (t _ C1)[S _ v4 _ v5 _ v6] = C0[S _ v1 _ v2 _ v3], value(v4), value(v5), value(v6), value(v1), value(v2), value(v3), context(C0), context(t _ C1) ⊦ (t _ C1)[v4 _ v6 _ (v5 _ v6)] = C0[v1 _ v3 _ (v2 _ v3)]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
⊦ (t1 _ C)[t] = t1 _ C[t]
Proof step 51:
t _ C1[S _ v4 _ v5 _ v6] = C0[S _ v1 _ v2 _ v3], value(v4), value(v5), value(v6), value(v1), value(v2), value(v3), context(C0), context(C1), value(t), ∀ 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)] ⊦ t _ C1[v4 _ v6 _ (v5 _ v6)] = C0[v1 _ v3 _ (v2 _ v3)]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ context(t _ C) ↔ ¬ ¬ (context(C) ∧ value(t))])]]