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Definition df-pmap 36680
Description: Define projective map for 𝑘 at 𝑎. Definition in Theorem 15.5 of [MaedaMaeda] p. 62. (Contributed by NM, 2-Oct-2011.)
Assertion
Ref Expression
df-pmap pmap = (𝑘 ∈ V ↦ (𝑎 ∈ (Base‘𝑘) ↦ {𝑝 ∈ (Atoms‘𝑘) ∣ 𝑝(le‘𝑘)𝑎}))
Distinct variable group:   𝑘,𝑎,𝑝

Detailed syntax breakdown of Definition df-pmap
StepHypRef Expression
1 cpmap 36673 . 2 class pmap
2 vk . . 3 setvar 𝑘
3 cvv 3471 . . 3 class V
4 va . . . 4 setvar 𝑎
52cv 1537 . . . . 5 class 𝑘
6 cbs 16461 . . . . 5 class Base
75, 6cfv 6328 . . . 4 class (Base‘𝑘)
8 vp . . . . . . 7 setvar 𝑝
98cv 1537 . . . . . 6 class 𝑝
104cv 1537 . . . . . 6 class 𝑎
11 cple 16550 . . . . . . 7 class le
125, 11cfv 6328 . . . . . 6 class (le‘𝑘)
139, 10, 12wbr 5039 . . . . 5 wff 𝑝(le‘𝑘)𝑎
14 catm 36439 . . . . . 6 class Atoms
155, 14cfv 6328 . . . . 5 class (Atoms‘𝑘)
1613, 8, 15crab 3130 . . . 4 class {𝑝 ∈ (Atoms‘𝑘) ∣ 𝑝(le‘𝑘)𝑎}
174, 7, 16cmpt 5119 . . 3 class (𝑎 ∈ (Base‘𝑘) ↦ {𝑝 ∈ (Atoms‘𝑘) ∣ 𝑝(le‘𝑘)𝑎})
182, 3, 17cmpt 5119 . 2 class (𝑘 ∈ V ↦ (𝑎 ∈ (Base‘𝑘) ↦ {𝑝 ∈ (Atoms‘𝑘) ∣ 𝑝(le‘𝑘)𝑎}))
191, 18wceq 1538 1 wff pmap = (𝑘 ∈ V ↦ (𝑎 ∈ (Base‘𝑘) ↦ {𝑝 ∈ (Atoms‘𝑘) ∣ 𝑝(le‘𝑘)𝑎}))
Colors of variables: wff setvar class
This definition is referenced by:  pmapfval  36932
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