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Proof step 8 from proof spawn-partial-corr-strng (previous step)

[:Inpf, S, Outf | SPAWN#(n; Inpf, S, Outf)], GInit(S), GInv(S), ¬ Prton(n)(S), ∀ m. Pr(m)(S) ⊦ (Rton(n)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(n)(S) ∧ GInv(S);Gton(n)(S, S') ∧ ¬ blocked ∧ (GInv(S) → GInv(S')))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ Prton(n)(s) ↔ (∀ m. m ≤ n → Pr(m)(s))
Proof step 10:
[:Inpf, S, Outf | SPAWN#(n; Inpf, S, Outf)], GInit(S), GInv(S), ∃ m. ¬(m ≤ n → Pr(m)(S)), ∀ m. Pr(m)(S) ⊦ (Rton(n)(S', S'') ∧ (GInv(S') → GInv(S''))) -+-> (last ⊃ Poton(n)(S) ∧ GInv(S);Gton(n)(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, n] flags: rewrite, current

Additional information

Used terms: S, n