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Proof step 10 from proof g-r (previous step)

CInv(n0, act0, cs0), CInv(n0, act, cs), Guar(n, cs, cs0), ∀ m0. m0 ≠ n → (act0(m0) ↔ act(m0)) ∧ (Idle(m0, cs) ↔ Idle(m0, cs0)), (¬ act(n) → Idle(n, cs)) → ¬ act0(n) → Idle(n, cs0) ⊦ m = n, Rely(m, cs, cs0) ∧ (Idle(m, cs) ↔ Idle(m, cs0)) ∧ (act0(m) ↔ act(m)), Inv(cs) ∧ Inv(cs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ CInv(m, act, cs) ↔ Inv(cs) ∧ (∀ m0. m < m0 → Idle(m0, cs) ∧ ¬ act(m0))
Proof step 12:
Inv(cs0) ∧ (∀ m0. n0 < m0 → Idle(m0, cs0) ∧ ¬ act0(m0)), CInv(n0, act, cs), Guar(n, cs, cs0), ∀ m0. m0 ≠ n → (act0(m0) ↔ act(m0)) ∧ (Idle(m0, cs) ↔ Idle(m0, cs0)), (¬ act(n) → Idle(n, cs)) → ¬ act0(n) → Idle(n, cs0) ⊦ m = n, Rely(m, cs, cs0) ∧ (Idle(m, cs) ↔ Idle(m, cs0)) ∧ (act0(m) ↔ act(m)), Inv(cs) ∧ Inv(cs0)

Rule argument

spec: CSPAWN+Preds inst: name: CInv-def seq: ⊦ CInv(m, act, cs) ↔ Inv(cs) ∧ (∀ m0. m < m0 → Idle(m0, cs) ∧ ¬ act(m0)) subst: [cs, act, m] → [cs0, act0, n0] flags: rewrite

Additional information

Used terms: cs0, act0, n0