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Proof step 23 from proof CSEQ-sat-rely-guar (previous step)

INDHYP-nat(n0), CInv(n, act, cs0), Idle(m, cs0), m ≤ n, ¬(CGuar(m, act, cs0, act(m; true), cs0) ∧ CInv(n, act(m; true), cs0)) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ 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 25:
INDHYP-nat(n0), CInv(n, act, cs0), Idle(m, cs0), m ≤ n, ( ¬ Guar(m, cs0, cs0) ∨ ¬((¬ act(m) → Idle(m, cs0)) → ¬ act(m; true)(m) → Idle(m, cs0)) ∨ (∃ m0. ¬(m0 ≠ m → (act(m; true)(m0) ↔ act(m0)) ∧ (Idle(m0, cs0) ↔ Idle(m0, cs0))))) ∨ ¬ CInv(n, act(m; true), 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, act(m; true), cs0, act, m] flags: rewrite

Additional information

Used terms: cs0, act(m; true), cs0, act, m