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Proof step 34 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), CRely(m, act(m; true), cs0, Act, CS), 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) ∧ Act(m) ∧ 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; { 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 35:
⊦ CRely(m, act1, cs1, act2, cs2) ↔ Rely(m, cs1, cs2) ∧ (Idle(m, cs1) ↔ Idle(m, cs2)) ∧ (act2(m) ↔ act1(m))
Proof step 36:
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, cs0) ↔ Idle(m, CS)) ∧ (Act(m) ↔ act(m; true)(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) ∧ Act(m) ∧ 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; { 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: CRely-def seq: ⊦ CRely(m, act1, cs1, act2, cs2) ↔ Rely(m, cs1, cs2) ∧ (Idle(m, cs1) ↔ Idle(m, cs2)) ∧ (act2(m) ↔ act1(m)) subst: [cs2, act2, cs1, act1, m] → [CS, Act, cs0, act(m; true), m] flags: rewrite

Additional information

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