| ∀ m0. m0 ≤ n0 + 1 → Pr(m0)(s), GInv(s), true, (¬(GInv(s) ∧ Pr(n0 + 1)(s)) ∧ ¬(GInv(s) ∧ Prton(n0)(s)) ∨ false ∨ false) ∨ ¬(GInv(s) ∧ Prton(n0)(s)) ∧ ¬(GInv(s) ∧ Pr(n0 + 1)(s)) ∨ false ∨ false, (true ⊃ ¬ Poton(n0 + 1)(s) ∨ ¬ GInv(s);¬ Gton(n0 + 1)(s, s) ∨ false ∨ ¬(GInv(s) → GInv(s))) ⊦ |
GInv(s), ¬ Pr(n0 + 1)(s) ∧ ¬ Prton(n0)(s) ∨ ¬ Prton(n0)(s) ∧ ¬ Pr(n0 + 1)(s), ∀ m0. m0 ≤ n0 + 1 → Pr(m0)(s) ⊦ Poton(n0 + 1)(s)