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Proof step 52 from proof CSEQ-sat-rely-guar (previous step)

INDHYP-nat(n0 + 1), m ≤ n, act(m), CInv(n, act, cs), boolvar → n0 = n1 ∧ act = act0 ∧ cs = cs0 ∧ outp = outp0 ∧ inp = inp0 ⊦ ( CInv(n, act0, cs0) ∧ act0(m) ∧ ¬ Act(m) ∧ CGuar(m, act, cs, 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) , {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)) ∧ ( Idle(m, cs) ∧ CRely(m, act, cs, act, cs) → ( act0 = (act(m; false)) ∧ outp = outp0 ∧ cs = cs0 ∧ inp = inp0 ∧ ¬ boolvar → CGuar(m, act, cs0, act(m; false), cs0) ∧ CInv(n, act(m; false), cs0)) ∧ ( act0 = (act(m; false)) ∧ outp = outp0 ∧ cs = cs0 ∧ inp = inp0 ∧ ¬ boolvar ∧ CGuar(m, act, cs0, act(m; false), cs0) ∧ CRely(m, act(m; false), cs0, Act, CS) ∧ n0 = N + 1 ∧ (CInv(n, act(m; false), 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) , { 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))) ∧ ( CInv(n, act0, cs0) ∧ act0(m) ∧ CInv(n, Act, CS) ∧ Act(m) ∧ CGuar(m, act, cs, act0, cs0) ∧ CRely(m, act0, cs0, Act, CS) ∧ n0 = N + 1 → [: Act, Inp, CS, Outp | (CRely(m, Act', CS', Act'', CS'') ∧ N = N'' + 1) , CGuar(m, Act, CS, Act', CS') , CInv(n, Act, CS) , {[PL (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 case distinction

And obtained the following new goals

Rule argument

pos: right 1

Additional information