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Proof step 4 from proof RG-restr-ok (previous step)

m < n ⊦ n = 0, (∀ act, cs, act4, cs4. ( (CInit(m + 1, act, cs) ∧ CInv(n, act, cs)) ∧ CRely(m + 1, act, cs, act4, cs4) ∧ (CInv(n, act, cs) → CInv(n, act4, cs4)) → CInit(m + 1, act4, cs4) ∧ CInv(n, act4, cs4)) ∧ ((CRely(m + 1, act, cs, act4, cs4) ∧ (CInv(n, act, cs) → CInv(n, act4, cs4))) ∧ CInv(n, act, cs) → CInv(n, act4, cs4)) ∧ ((CRelyto(m, act, cs, act4, cs4) ∧ (CInv(n, act, cs) → CInv(n, act4, cs4))) ∧ CInv(n, act, cs) → CInv(n, act4, cs4)) ∧ ( (CInitto(m, act, cs) ∧ CInv(n, act, cs)) ∧ CRelyto(m, act, cs, act4, cs4) ∧ (CInv(n, act, cs) → CInv(n, act4, cs4)) → CInitto(m, act4, cs4) ∧ CInv(n, act4, cs4)) ∧ ( (CGuar(m + 1, act, cs, act4, cs4) ∧ (CInv(n, act, cs) → CInv(n, act4, cs4))) ∧ CInv(n, act, cs) → CRelyto(m, act, cs, act4, cs4) ∧ (CInv(n, act, cs) → CInv(n, act4, cs4))) ∧ ( (CGuarto(m, act, cs, act4, cs4) ∧ (CInv(n, act, cs) → CInv(n, act4, cs4))) ∧ CInv(n, act, cs) → CRely(m + 1, act, cs, act4, cs4) ∧ (CInv(n, act, cs) → CInv(n, act4, cs4)))) ∧ (∀ act, cs, act4, cs4, act5, cs5. ( (CInit(m + 1, act, cs) ∧ CInv(n, act, cs)) ∧ CInv(n, act4, cs4) ∧ CInv(n, act4, cs4) ∧ CRely(m + 1, act4, cs4, act5, cs5) ∧ (CInv(n, act4, cs4) → CInv(n, act5, cs5)) → CInv(n, act5, cs5)) ∧ ( (CInitto(m, act, cs) ∧ CInv(n, act, cs)) ∧ CInv(n, act4, cs4) ∧ CInv(n, act4, cs4) ∧ CRelyto(m, act4, cs4, act5, cs5) ∧ (CInv(n, act4, cs4) → CInv(n, act5, cs5)) → CInv(n, act5, cs5)) ∧ ( (CRely(m + 1, act, cs, act4, cs4) ∧ (CInv(n, act, cs) → CInv(n, act4, cs4))) ∧ (CRely(m + 1, act4, cs4, act5, cs5) ∧ (CInv(n, act4, cs4) → CInv(n, act5, cs5))) ∧ CInv(n, act, cs) → CRely(m + 1, act, cs, act5, cs5) ∧ (CInv(n, act, cs) → CInv(n, act5, cs5))) ∧ ( (CRelyto(m, act, cs, act4, cs4) ∧ (CInv(n, act, cs) → CInv(n, act4, cs4))) ∧ (CRelyto(m, act4, cs4, act5, cs5) ∧ (CInv(n, act4, cs4) → CInv(n, act5, cs5))) ∧ CInv(n, act, cs) → CRelyto(m, act, cs, act5, cs5) ∧ (CInv(n, act, cs) → CInv(n, act5, cs5)))) ∧ (∀ act, cs. ( CInv(n, act, cs) → (CRely(m + 1, act, cs, act, cs) ∧ (CInv(n, act, cs) → CInv(n, act, cs))) ∧ CRelyto(m, act, cs, act, cs) ∧ (CInv(n, act, cs) → CInv(n, act, cs))) ∧ (CInit(m + 1, act, cs) ∧ CInv(n, act, cs) → CInv(n, act, cs)) ∧ (CInitto(m, act, cs) ∧ CInv(n, act, cs) → CInv(n, act, cs)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
m < n ⊦ n = 0, (CInit(m + 1, act, cs) ∧ CInv(n, act, cs) ∧ CRely(m + 1, act, cs, act0, cs0) ∧ CInv(n, act0, cs0) → CInit(m + 1, act0, cs0)) ∧ (CInitto(m, act, cs) ∧ CInv(n, act, cs) ∧ CRelyto(m, act, cs, act0, cs0) ∧ CInv(n, act0, cs0) → CInitto(m, act0, cs0)) ∧ (CGuar(m + 1, act, cs, act0, cs0) ∧ CInv(n, act0, cs0) ∧ CInv(n, act, cs) → CRelyto(m, act, cs, act0, cs0)) ∧ (CGuarto(m, act, cs, act0, cs0) ∧ CInv(n, act0, cs0) ∧ CInv(n, act, cs) → CRely(m + 1, act, cs, act0, cs0)) ∧ ( CRely(m + 1, act1, cs1, act2, cs2) ∧ CInv(n, act2, cs2) ∧ CRely(m + 1, act2, cs2, act3, cs3) ∧ CInv(n, act3, cs3) ∧ CInv(n, act1, cs1) → CRely(m + 1, act1, cs1, act3, cs3)) ∧ ( CRelyto(m, act1, cs1, act2, cs2) ∧ CInv(n, act2, cs2) ∧ CRelyto(m, act2, cs2, act3, cs3) ∧ CInv(n, act3, cs3) ∧ CInv(n, act1, cs1) → CRelyto(m, act1, cs1, act3, cs3)) ∧ (CInv(n, act4, cs4) → CRelyto(m, act4, cs4, act4, cs4))

Rule argument

Additional information

Used simplifier rules: CRely-refl: ⊦ CInv(n, act, cs) → (¬ CRely(m, act, cs, act, cs) ↔ false);