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Proof step 66 from proof RG-restr-ok (previous step)

m0 < n, Guar(m0, cs, cs0), m0 ≤ m, CInv(n, act0, cs0), CInv(n, act, cs), m < n, ∀ m1. m1 ≠ m0 → (act0(m1) ↔ act(m1)) ∧ (Idle(m1, cs) ↔ Idle(m1, cs0)), (¬ act(m0) → Idle(m0, cs)) → ¬ act0(m0) → Idle(m0, cs0) ⊦ n = 0, m0 = m + 1, Rely(m + 1, cs, cs0) ∧ (Idle(m + 1, cs) ↔ Idle(m + 1, cs0)) ∧ (act0(m + 1) ↔ act(m + 1)), Inv(cs0) ∧ Inv(cs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ CInv(m, act, cs) ↔ Inv(cs) ∧ (∀ m0. m < m0 → Idle(m0, cs) ∧ ¬ act(m0))
Proof step 68:
m0 < n, Guar(m0, cs, cs0), m0 ≤ m, CInv(n, act0, cs0), Inv(cs) ∧ (∀ m0. n < m0 → Idle(m0, cs) ∧ ¬ act(m0)), m < n, ∀ m1. m1 ≠ m0 → (act0(m1) ↔ act(m1)) ∧ (Idle(m1, cs) ↔ Idle(m1, cs0)), (¬ act(m0) → Idle(m0, cs)) → ¬ act0(m0) → Idle(m0, cs0) ⊦ n = 0, m0 = m + 1, Rely(m + 1, cs, cs0) ∧ (Idle(m + 1, cs) ↔ Idle(m + 1, cs0)) ∧ (act0(m + 1) ↔ act(m + 1)), 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] → [cs, act, n] flags: rewrite

Additional information

Used terms: cs, act, n