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Proof step 53 from proof subst-SS-equal (conclusion)

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

User applied rule structural induction

And obtained the following new goals

Proof step 20:
O[S _ v4 _ v5 _ v6] = C0[S _ v1 _ v2 _ v3], value(v4), value(v5), value(v6), value(v1), value(v2), value(v3), context(C0), context(O) ⊦ O[v4 _ v6 _ (v5 _ v6)] = C0[v1 _ v3 _ (v2 _ v3)]
Proof step 42:
∀ 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)], (C1 _ t)[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 _ t) ⊦ (C1 _ t)[v4 _ v6 _ (v5 _ v6)] = C0[v1 _ v3 _ (v2 _ v3)]
Proof step 52:
∀ 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)]

Rule argument

[VARWITHVARSEQSARG : C, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : rawctxt generated by o, _, _;])]]