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Proof step 40 from proof rg-restr1 (previous step)

⊦ (∀ m. m ≤ n0 → Ry(m)(s1, s2)) ∧ (∀ m. m ≤ n0 → Ry(m)(s2, s3)) → Rton(n0)(s1, s3)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ Rton(n)(s, s0) ↔ (∀ m. m ≤ n → Ry(m)(s, s0))
Proof step 42:
⊦ (∀ m. m ≤ n0 → Ry(m)(s1, s2)) ∧ (∀ m. m ≤ n0 → Ry(m)(s2, s3)) → (∀ m. m ≤ n0 → Ry(m)(s1, s3))

Rule argument

spec: inst: name: rton-def seq: ⊦ Rton(n)(s, s0) ↔ (∀ m. m ≤ n → Ry(m)(s, s0)) subst: [s0, s, n] → [s3, s1, n0] flags: rewrite, current

Additional information

Used terms: s3, s1, n0