Metamath Proof Explorer

Theorem sthil

Description: The value of a state at the full Hilbert space. (Contributed by NM, 23-Oct-1999) (New usage is discouraged.)

Ref Expression
Assertion sthil 
|- ( S e. States -> ( S ` ~H ) = 1 )

Proof

Step Hyp Ref Expression
1 isst 
 |-  ( S e. States <-> ( S : CH --> ( 0 [,] 1 ) /\ ( S ` ~H ) = 1 /\ A. x e. CH A. y e. CH ( x C_ ( _|_ ` y ) -> ( S ` ( x vH y ) ) = ( ( S ` x ) + ( S ` y ) ) ) ) )
2 1 simp2bi 
 |-  ( S e. States -> ( S ` ~H ) = 1 )