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generic specification
parameter
state
using nat
target
predicates RG-restr
: (state → bool) × (state → bool) × (state × state → bool) × (state × state → bool) × (state → bool) × (state → bool) × (state → bool) ×
(state × state → bool) × (state × state → bool) × (state → bool) × (state → bool) × (state → bool)
;
variables bv : bool;
R : state × state → bool;
G : state × state → bool;
R1 : state × state → bool;
G1 : state × state → bool;
R2 : state × state → bool;
G2 : state × state → bool;
Init : state → bool;
Inv : state → bool;
Pre : state → bool;
Pre1 : state → bool;
Pre2 : state → bool;
Post : state → bool;
Post1 : state → bool;
Post2 : state → bool;
Runs : state → bool;
Runs1 : state → bool;
Runs2 : state → bool;
N : nat flexible;
axioms RG-restr-def
: ⊦ RG-restr(Init, Inv, R1, G1, Pre1, Post1, Runs1, R2, G2, Pre2, Post2, Runs2)
↔ (∀ s, s0.
(G1(s, s0) → R2(s, s0)) ∧ (G2(s, s0) → R1(s, s0)) ∧ (Pre1(s) ∧ R1(s, s0) → Pre1(s0)) ∧ (Pre2(s) ∧ R2(s, s0) → Pre2(s0))
∧ (Post1(s) ∧ R1(s, s0) → Post1(s0)) ∧ (Post2(s) ∧ R2(s, s0) → Post2(s0)))
∧ (∀ s, s0, s1. (R1(s, s0) ∧ R1(s0, s1) → R1(s, s1)) ∧ (R2(s, s0) ∧ R2(s0, s1) → R2(s, s1)))
∧ (∀ s.
(∃ s. Init(s)) ∧ (Init(s) → Pre1(s) ∧ Pre2(s) ∧ Inv(s)) ∧ R1(s, s) ∧ R2(s, s) ∧ (Inv(s) → Runs1(s) ∨ Runs2(s))
∧ (Post1(s) → Runs2(s)) ∧ (Post2(s) → Runs1(s)));
end generic specification