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Proof step 37 from proof CSEQ-sat-rely-guar (previous step)

INDHYP-nat(N + 1), CInv(n, act, cs0), Idle(m, cs0), m ≤ n, CGuar(m, act, cs0, act(m; true), cs0), Rely(m, cs0, CS), Idle(m, CS), Act(m), CInv(n, act(m; true), cs0) → CInv(n, Act, CS) ⊦ [: Act, Inp, CS, Outp | (CRely(m, Act', CS', Act'', CS'') ∧ N = N'' + 1) , CGuar(m, Act, CS, Act', CS') , CInv(n, Act, CS) , {[PL CInv(n, Act, CS) → (CRely(m, Act', CS', Act'', CS'') ∧ (CInv(n, Act', CS') ∧ Act'(m) → CInv(n, Act'', CS'') ∧ Act''(m))) -+-> (last ⊃ CInv(n, Act, CS) ∧ Idle(m, CS) ∧ Act(m) ;CGuar(m, Act, CS, Act', CS') ∧ (CInv(n, Act, CS) ∧ Act(m) → CInv(n, Act', CS') ∧ Act'(m)) ) ]; Act(m) := false; { skip or {Act(m) := true; [PL CInv(n, Act, CS) ∧ Act(m) ∧ m ≤ n ∧ Idle(m, CS) → (CRely(m, Act', CS', Act'', CS'') ∧ (CInv(n, Act', CS') ∧ Act'(m) → CInv(n, Act'', CS'') ∧ Act''(m))) -+-> (last ⊃ CInv(n, Act, CS) ∧ Idle(m, CS) ∧ Act(m) ;CGuar(m, Act, CS, Act', CS') ∧ (CInv(n, Act, CS) ∧ Act(m) → CInv(n, Act', CS') ∧ Act'(m)) ) ]; Act(m) := false}} star} ] CInv(n, Act, CS)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ 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 39:
INDHYP-nat(N + 1), 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))), Rely(m, cs0, CS), Idle(m, CS), Act(m), CInv(n, act(m; true), cs0) → CInv(n, Act, CS) ⊦ [: Act, Inp, CS, Outp | (CRely(m, Act', CS', Act'', CS'') ∧ N = N'' + 1) , CGuar(m, Act, CS, Act', CS') , CInv(n, Act, CS) , {[PL CInv(n, Act, CS) → (CRely(m, Act', CS', Act'', CS'') ∧ (CInv(n, Act', CS') ∧ Act'(m) → CInv(n, Act'', CS'') ∧ Act''(m))) -+-> (last ⊃ CInv(n, Act, CS) ∧ Idle(m, CS) ∧ Act(m) ;CGuar(m, Act, CS, Act', CS') ∧ (CInv(n, Act, CS) ∧ Act(m) → CInv(n, Act', CS') ∧ Act'(m)) ) ]; Act(m) := false; { skip or {Act(m) := true; [PL CInv(n, Act, CS) ∧ Act(m) ∧ m ≤ n ∧ Idle(m, CS) → (CRely(m, Act', CS', Act'', CS'') ∧ (CInv(n, Act', CS') ∧ Act'(m) → CInv(n, Act'', CS'') ∧ Act''(m))) -+-> (last ⊃ CInv(n, Act, CS) ∧ Idle(m, CS) ∧ Act(m) ;CGuar(m, Act, CS, Act', CS') ∧ (CInv(n, Act, CS) ∧ Act(m) → CInv(n, Act', CS') ∧ Act'(m)) ) ]; Act(m) := false}} star} ] CInv(n, Act, CS)

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