| INDHYP-nat(n0), CInv(n, act, cs), Idle(m, cs), m ≤ n, boolvar → n0 = n1 ∧ act = act0 ∧ cs = cs0 ∧ outp = outp0 ∧ inp = inp0, outp = outp0, cs = cs0, inp = inp0, act = act0, ¬ boolvar, CGuar(m, act0, cs0, act0, cs0), CRely(m, act0, cs0, Act, CS), n0 = N + 1, 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) , { 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) |
INDHYP-nat(N + 1), CInv(n, act0, cs0), Idle(m, cs0), m ≤ n, CGuar(m, act0, cs0, act0, cs0), CRely(m, act0, cs0, Act, CS), 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) , { 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)