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Proof step 10 from proof rg-restr1 (previous step)

Gr(n0 + 1)(s, s0), m ≤ n0 ⊦ Ry(m)(s, s0)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 11:
⊦ Gr(m)(s, s0) → (∀ n. n ≠ m → Ry(n)(s, s0))
Proof step 12:
Gr(n0 + 1)(s, s0) → (∀ n. n ≠ n0 + 1 → Ry(n)(s, s0)), Gr(n0 + 1)(s, s0), m ≤ n0 ⊦ Ry(m)(s, s0)

Rule argument

spec: RGn inst: name: g-r seq: ⊦ Gr(m)(s, s0) → (∀ n. n ≠ m → Ry(n)(s, s0)) subst: [m, s, s0] → [n0 + 1, s, s0] flags: []

Additional information

Used terms: n0 + 1, s, s0