Description: Domain of the partial isomorphism C. (Contributed by NM, 8-Mar-2014) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | dicfn.l | ⊢ ≤ = ( le ‘ 𝐾 ) | |
dicfn.a | ⊢ 𝐴 = ( Atoms ‘ 𝐾 ) | ||
dicfn.h | ⊢ 𝐻 = ( LHyp ‘ 𝐾 ) | ||
dicfn.i | ⊢ 𝐼 = ( ( DIsoC ‘ 𝐾 ) ‘ 𝑊 ) | ||
Assertion | dicdmN | ⊢ ( ( 𝐾 ∈ 𝑉 ∧ 𝑊 ∈ 𝐻 ) → dom 𝐼 = { 𝑝 ∈ 𝐴 ∣ ¬ 𝑝 ≤ 𝑊 } ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dicfn.l | ⊢ ≤ = ( le ‘ 𝐾 ) | |
2 | dicfn.a | ⊢ 𝐴 = ( Atoms ‘ 𝐾 ) | |
3 | dicfn.h | ⊢ 𝐻 = ( LHyp ‘ 𝐾 ) | |
4 | dicfn.i | ⊢ 𝐼 = ( ( DIsoC ‘ 𝐾 ) ‘ 𝑊 ) | |
5 | 1 2 3 4 | dicfnN | ⊢ ( ( 𝐾 ∈ 𝑉 ∧ 𝑊 ∈ 𝐻 ) → 𝐼 Fn { 𝑝 ∈ 𝐴 ∣ ¬ 𝑝 ≤ 𝑊 } ) |
6 | 5 | fndmd | ⊢ ( ( 𝐾 ∈ 𝑉 ∧ 𝑊 ∈ 𝐻 ) → dom 𝐼 = { 𝑝 ∈ 𝐴 ∣ ¬ 𝑝 ≤ 𝑊 } ) |