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 ∈ States → ( 𝑆 ‘ ℋ ) = 1 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isst | ⊢ ( 𝑆 ∈ States ↔ ( 𝑆 : Cℋ ⟶ ( 0 [,] 1 ) ∧ ( 𝑆 ‘ ℋ ) = 1 ∧ ∀ 𝑥 ∈ Cℋ ∀ 𝑦 ∈ Cℋ ( 𝑥 ⊆ ( ⊥ ‘ 𝑦 ) → ( 𝑆 ‘ ( 𝑥 ∨ℋ 𝑦 ) ) = ( ( 𝑆 ‘ 𝑥 ) + ( 𝑆 ‘ 𝑦 ) ) ) ) ) | |
2 | 1 | simp2bi | ⊢ ( 𝑆 ∈ States → ( 𝑆 ‘ ℋ ) = 1 ) |