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Proof step 111 from proof RG-restr-ok (previous step)

act3(m0) ↔ act1(m0), Idle(m0, cs2) ↔ Idle(m0, cs3), Idle(m0, cs1) ↔ Idle(m0, cs3), act2(m0) ↔ act1(m0), Rely(m0, cs1, cs2), Rely(m0, cs2, cs3), m0 < n, CInv(n, act2, cs2), CInv(n, act3, cs3), CInv(n, act1, cs1), m < n, m0 ≤ m ⊦ n = 0, Rely(m0, cs1, cs3)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 112:
⊦ Rely(m, cs1, cs2) ∧ Rely(m, cs2, cs3) ∧ Inv(cs1) → Rely(m, cs1, cs3)
Proof step 113:
¬(Rely(m0, cs1, cs2) ∧ Rely(m0, cs2, cs3) ∧ Inv(cs1)), act3(m0) ↔ act1(m0), Idle(m0, cs2) ↔ Idle(m0, cs3), Idle(m0, cs1) ↔ Idle(m0, cs3), act2(m0) ↔ act1(m0), Rely(m0, cs1, cs2), Rely(m0, cs2, cs3), m0 < n, CInv(n, act2, cs2), CInv(n, act3, cs3), CInv(n, act1, cs1), m < n, m0 ≤ m ⊦ n = 0, Rely(m0, cs1, cs3)

Rule argument

spec: RGI-Conds inst: name: r-trans seq: ⊦ Rely(m, cs1, cs2) ∧ Rely(m, cs2, cs3) ∧ Inv(cs1) → Rely(m, cs1, cs3) subst: [cs2, cs3, cs1, m] → [cs2, cs3, cs1, m0] flags: rewrite

Additional information

Used terms: cs2, cs3, cs1, m0