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Proof step 31 from proof COP-sat-rely-guar (previous step)

□ (Act = Act' ∧ Inp = Inp'), boolvar ∨ n0 = N + 1 ∧ N = N'' + 1 until Boolvar, Rely(m, cs0, CS) ∧ (Idle(m, cs0) ↔ Idle(m, CS)) ∧ Inv(CS) → (Rely(m, CS', CS'') ∧ (Idle(m, CS') ↔ Idle(m, CS'')) ∧ (Inv(CS') → Inv(CS''))) -+-> (last ⊃ Idle(m, CS) ∧ Inv(CS);Guar(m, CS, CS') ∧ (∀ m0. m0 ≠ m → (Idle(m0, CS) ↔ Idle(m0, CS'))) ∧ (Inv(CS) → Inv(CS'))), INDHYP-nat(n0), Guar(m, cs, cs0), m ≤ n, act0(m), Inv(cs), Inv(cs0), ¬ CInv(n, act0, cs0), ∀ m1. m1 ≠ m → (Idle(m1, cs) ↔ Idle(m1, cs0)), ∀ m0. n < m0 → Idle(m0, cs) ∧ ¬ act0(m0) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ CInv(m, act, cs) ↔ Inv(cs) ∧ (∀ m0. m < m0 → Idle(m0, cs) ∧ ¬ act(m0))
Proof step 33:
Rely(m, cs0, CS) ∧ (Idle(m, cs0) ↔ Idle(m, CS)) ∧ Inv(CS) → (Rely(m, CS', CS'') ∧ (Idle(m, CS') ↔ Idle(m, CS'')) ∧ (Inv(CS') → Inv(CS''))) -+-> (last ⊃ Idle(m, CS) ∧ Inv(CS);Guar(m, CS, CS') ∧ (∀ m0. m0 ≠ m → (Idle(m0, CS) ↔ Idle(m0, CS'))) ∧ (Inv(CS) → Inv(CS'))), boolvar ∨ n0 = N + 1 ∧ N = N'' + 1 until Boolvar, □ (Act = Act' ∧ Inp = Inp'), INDHYP-nat(n0), Guar(m, cs, cs0), m ≤ n, act0(m), Inv(cs), Inv(cs0), ¬ Inv(cs0) ∨ (∃ m0. ¬(n < m0 → Idle(m0, cs0) ∧ ¬ act0(m0))), ∀ m1. m1 ≠ m → (Idle(m1, cs) ↔ Idle(m1, cs0)), ∀ m0. n < m0 → Idle(m0, cs) ∧ ¬ act0(m0) ⊦

Rule argument

spec: CSPAWN 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