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Proof step 23 from proof fair-always-left-relyinv (previous step)

□ (CRelyto(n + 1, Act', CS', Act'', CS'') ∧ CInv(n0, Act', CS') ∧ CInv(n0, Act'', CS'')), [:Act, CS | [PL ◇ (¬ CRely(n + 1, Act', CS', Act'', CS'') ∨ ¬(CInv(n0, Act', CS') → CInv(n0, Act'', CS''))) ∧ (CRely(n + 1, Act', CS', Act'', CS'') ∧ (CInv(n0, Act', CS') → CInv(n0, Act'', CS''))) -+-> (last ⊃ CInv(n0, Act, CS);CGuar(n + 1, Act, CS, Act', CS') ∧ (CInv(n0, Act, CS) → CInv(n0, Act', CS'))) ] ∥ [PL (CRelyto(n, Act', CS', Act'', CS'') ∧ (CInv(n0, Act', CS') → CInv(n0, Act'', CS''))) -+-> (last ⊃ CInv(n0, Act, CS);CGuarto(n, Act, CS, Act', CS') ∧ (CInv(n0, Act, CS) → CInv(n0, Act', CS'))) ] ], n0 ≠ 0, m ≤ n, Init(cs), RG-restr (n0, λ n0, act, cs, act0, cs0. CRely(n + 1, act, cs, act0, cs0) ∧ (CInv(n0, act, cs) → CInv(n0, act0, cs0)), λ n0, act, cs, act0, cs0. CGuar(n + 1, act, cs, act0, cs0) ∧ (CInv(n0, act, cs) → CInv(n0, act0, cs0)), λ n0, act, cs. CInit(n + 1, act, cs) ∧ CInv(n0, act, cs), λ n, act, cs, act0, cs0. CInv(n, act0, cs0), CInv, λ n0, act, cs, act0, cs0. CRelyto(n, act, cs, act0, cs0) ∧ (CInv(n0, act, cs) → CInv(n0, act0, cs0)), λ n0, act, cs, act0, cs0. CGuarto(n, act, cs, act0, cs0) ∧ (CInv(n0, act, cs) → CInv(n0, act0, cs0)), λ n0, act, cs. CInitto(n, act, cs) ∧ CInv(n0, act, cs), λ n, act, cs, act0, cs0. CInv(n, act0, cs0)), CInv(n0, Act, CS), n < n0, m < n0, ¬ CInit(m, λ n. false, cs), ∀ n. Idle(n, cs) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ CInit(m, act1, cs1) ↔ Idle(m, cs1) ∧ ¬ act1(m)
Proof step 25:
[:Act, CS | [PL ◇ (¬ CRely(n + 1, Act', CS', Act'', CS'') ∨ ¬(CInv(n0, Act', CS') → CInv(n0, Act'', CS''))) ∧ (CRely(n + 1, Act', CS', Act'', CS'') ∧ (CInv(n0, Act', CS') → CInv(n0, Act'', CS''))) -+-> (last ⊃ CInv(n0, Act, CS);CGuar(n + 1, Act, CS, Act', CS') ∧ (CInv(n0, Act, CS) → CInv(n0, Act', CS'))) ] ∥ [PL (CRelyto(n, Act', CS', Act'', CS'') ∧ (CInv(n0, Act', CS') → CInv(n0, Act'', CS''))) -+-> (last ⊃ CInv(n0, Act, CS);CGuarto(n, Act, CS, Act', CS') ∧ (CInv(n0, Act, CS) → CInv(n0, Act', CS'))) ] ], □ (CRelyto(n + 1, Act', CS', Act'', CS'') ∧ CInv(n0, Act', CS') ∧ CInv(n0, Act'', CS'')), n0 ≠ 0, m ≤ n, Init(cs), RG-restr (n0, λ n0, act, cs, act0, cs0. CRely(n + 1, act, cs, act0, cs0) ∧ (CInv(n0, act, cs) → CInv(n0, act0, cs0)), λ n0, act, cs, act0, cs0. CGuar(n + 1, act, cs, act0, cs0) ∧ (CInv(n0, act, cs) → CInv(n0, act0, cs0)), λ n0, act, cs. CInit(n + 1, act, cs) ∧ CInv(n0, act, cs), λ n, act, cs, act0, cs0. CInv(n, act0, cs0), CInv, λ n0, act, cs, act0, cs0. CRelyto(n, act, cs, act0, cs0) ∧ (CInv(n0, act, cs) → CInv(n0, act0, cs0)), λ n0, act, cs, act0, cs0. CGuarto(n, act, cs, act0, cs0) ∧ (CInv(n0, act, cs) → CInv(n0, act0, cs0)), λ n0, act, cs. CInitto(n, act, cs) ∧ CInv(n0, act, cs), λ n, act, cs, act0, cs0. CInv(n, act0, cs0)), CInv(n0, Act, CS), n < n0, m < n0, ¬ Idle(m, cs) ∨ false, ∀ n. Idle(n, cs) ⊦

Rule argument

spec: CSPAWN+Preds inst: name: CInit-def seq: ⊦ CInit(m, act1, cs1) ↔ Idle(m, cs1) ∧ ¬ act1(m) subst: [cs1, act1, m] → [cs, λ n. false, m] flags: rewrite

Additional information

Used terms: cs, λ n. false, m