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Proof step 8 from proof CSPAWN-sat-rely-guar (previous step)

Init(CS), ∀ n0. ¬ Act(n0), ¬(m ≤ n → CInit(m, Act, CS)) ∨ ¬ CInv(n, Act, CS) ⊦ [: Act, Inp, CS, Outp | CRelyto(n, Act', CS', Act'', CS'') , CGuarto(n, Act, CS, Act', CS') , CInv(n, Act, CS) , CSPAWN(n; Act, Inp, CS, Outp) ] CInv(n, Act, CS)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ CInv(m, act, cs) ↔ Inv(cs) ∧ (∀ m0. m < m0 → Idle(m0, cs) ∧ ¬ act(m0))
Proof step 10:
Init(CS), ∀ n0. ¬ Act(n0), ¬(m ≤ n → CInit(m, Act, CS)) ∨ ¬(Inv(CS) ∧ (∀ m0. n < m0 → Idle(m0, CS) ∧ ¬ Act(m0))) ⊦ [: Act, Inp, CS, Outp | CRelyto(n, Act', CS', Act'', CS'') , CGuarto(n, Act, CS, Act', CS') , (Inv(CS) ∧ (∀ m0. n < m0 → Idle(m0, CS) ∧ ¬ Act(m0))) , CSPAWN(n; Act, Inp, CS, Outp) ] (Inv(CS) ∧ (∀ m0. n < m0 → Idle(m0, CS) ∧ ¬ Act(m0)))

Rule argument

spec: CSPAWN inst: name: CInv-def seq: ⊦ CInv(m, act, cs) ↔ Inv(cs) ∧ (∀ m0. m < m0 → Idle(m0, cs) ∧ ¬ act(m0)) subst: [cs, act, m] → [CS, Act, n] flags: rewrite

Additional information

Used terms: CS, Act, n