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Proof step 34 from proof spawn-sat-rg-strnger (previous step)

[:Inpf, S, Outf | [PL ¬ GInv(S) ∨ ¬ Pr(n0 + 1)(S)] ∥ [PL ¬ GInv(S) ∨ ¬ Prton(n0)(S)]], Prton(n0 + 1)(S), GInv(S) ⊦ (Rton(n0 + 1)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(n0 + 1)(S) ∧ GInv(S);Gton(n0 + 1)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ Prton(n)(s) ↔ (∀ m. m ≤ n → Pr(m)(s))
Proof step 36:
[:Inpf, S, Outf | [PL ¬ GInv(S) ∨ ¬ Pr(n0 + 1)(S)] ∥ [PL ¬ GInv(S) ∨ ¬ Prton(n0)(S)]], ∀ m. m ≤ n0 + 1 → Pr(m)(S), GInv(S) ⊦ (Rton(n0 + 1)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(n0 + 1)(S) ∧ GInv(S);Gton(n0 + 1)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))

Rule argument

spec: inst: name: prton-def seq: ⊦ Prton(n)(s) ↔ (∀ m. m ≤ n → Pr(m)(s)) subst: [s, n] → [S, n0 + 1] flags: rewrite, current

Additional information

Used terms: S, n0 + 1