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Proof step 47 from proof RG-restr-ok (previous step)

m0 < n, Guar(m + 1, cs, cs0), CInv(n, act0, cs0), CInv(n, act, cs), m < n, m0 ≤ m, ∀ m0. m0 ≠ m + 1 → (act0(m0) ↔ act(m0)) ∧ (Idle(m0, cs) ↔ Idle(m0, cs0)), (¬ act(m + 1) → Idle(m + 1, cs)) → ¬ act0(m + 1) → Idle(m + 1, cs0) ⊦ n = 0, m + 1 = m0, Rely(m0, cs, cs0) ∧ (Idle(m0, cs) ↔ Idle(m0, cs0)) ∧ (act0(m0) ↔ act(m0)), Inv(cs0) ∧ Inv(cs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ CInv(m, act, cs) ↔ Inv(cs) ∧ (∀ m0. m < m0 → Idle(m0, cs) ∧ ¬ act(m0))
Proof step 49:
m0 < n, Guar(m + 1, cs, cs0), Inv(cs0) ∧ (∀ m0. n < m0 → Idle(m0, cs0) ∧ ¬ act0(m0)), CInv(n, act, cs), m < n, m0 ≤ m, ∀ m0. m0 ≠ m + 1 → (act0(m0) ↔ act(m0)) ∧ (Idle(m0, cs) ↔ Idle(m0, cs0)), (¬ act(m + 1) → Idle(m + 1, cs)) → ¬ act0(m + 1) → Idle(m + 1, cs0) ⊦ n = 0, m + 1 = m0, Rely(m0, cs, cs0) ∧ (Idle(m0, cs) ↔ Idle(m0, cs0)) ∧ (act0(m0) ↔ act(m0)), Inv(cs0) ∧ Inv(cs)

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, n] flags: rewrite

Additional information

Used terms: cs0, act0, n