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Proof step 2 from proof g-r (previous step)

CGuar(n, act, cs, act0, cs0), CInv(n0, act, cs), CInv(n0, act0, cs0) ⊦ m = n, CRely(m, act, cs, act0, cs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ CGuar(m, act, cs, act0, cs0) ↔ Guar(m, cs, cs0) ∧ ((¬ act(m) → Idle(m, cs)) → ¬ act0(m) → Idle(m, cs0)) ∧ (∀ m0. m0 ≠ m → (act0(m0) ↔ act(m0)) ∧ (Idle(m0, cs) ↔ Idle(m0, cs0)))
Proof step 4:
Guar(n, cs, cs0) ∧ ((¬ act(n) → Idle(n, cs)) → ¬ act0(n) → Idle(n, cs0)) ∧ (∀ m0. m0 ≠ n → (act0(m0) ↔ act(m0)) ∧ (Idle(m0, cs) ↔ Idle(m0, cs0))), CInv(n0, act, cs), CInv(n0, act0, cs0) ⊦ m = n, CRely(m, act, cs, act0, cs0)

Rule argument

spec: CSPAWN+Preds inst: name: CGuar-def seq: ⊦ CGuar(m, act, cs, act0, cs0) ↔ Guar(m, cs, cs0) ∧ ((¬ act(m) → Idle(m, cs)) → ¬ act0(m) → Idle(m, cs0)) ∧ (∀ m0. m0 ≠ m → (act0(m0) ↔ act(m0)) ∧ (Idle(m0, cs) ↔ Idle(m0, cs0))) subst: [cs0, act0, cs, act, m] → [cs0, act0, cs, act, n] flags: rewrite

Additional information

Used terms: cs0, act0, cs, act, n