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Proof step 5 from proof rg-restr2 (previous step)

⊦ (Gr(n0 + 1)(s, s0) → Rton(n0)(s, s0)) ∧ (Gton(n0)(s, s0) → Ry(n0 + 1)(s, s0)) ∧ (Prton(n0)(s) ∧ Rton(n0)(s, s0) → Prton(n0)(s0)) ∧ (Poton(n0)(s) ∧ Rton(n0)(s, s0) → Poton(n0)(s0)) ∧ (Ry(n0 + 1)(s1, s2) ∧ Ry(n0 + 1)(s2, s3) → Ry(n0 + 1)(s1, s3)) ∧ (Rton(n0)(s1, s2) ∧ Rton(n0)(s2, s3) → Rton(n0)(s1, s3)) ∧ (∃ s. GInit(s)) ∧ (GInit(s4) → Pr(n0 + 1)(s4) ∧ Prton(n0)(s4) ∧ GInv(s4)) ∧ Ry(n0 + 1)(s4, s4) ∧ Rton(n0)(s4, s4)

User applied rule case distinction

And obtained the following new goals

Proof step 6:
⊦ Gr(n0 + 1)(s, s0) → Rton(n0)(s, s0)
Proof step 14:
⊦ Gton(n0)(s, s0) → Ry(n0 + 1)(s, s0)
Proof step 22:
⊦ Prton(n0)(s) ∧ Rton(n0)(s, s0) → Prton(n0)(s0)
Proof step 33:
⊦ Poton(n0)(s) ∧ Rton(n0)(s, s0) → Poton(n0)(s0)
Proof step 44:
⊦ Rton(n0)(s1, s2) ∧ Rton(n0)(s2, s3) → Rton(n0)(s1, s3)
Proof step 55:
⊦ ∃ s. GInit(s)
Proof step 57:
⊦ GInit(s4) → Pr(n0 + 1)(s4) ∧ Prton(n0)(s4) ∧ GInv(s4)
Proof step 67:
⊦ Ry(n0 + 1)(s4, s4)
Proof step 71:
⊦ Rton(n0)(s4, s4)

Rule argument

pos: right 1

Additional information

Used simplifier rules: r-trans: ⊦ Ry(m)(s, s0) ∧ Ry(m)(s0, s1) → Ry(m)(s, s1); (forward) from specification RGn