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Definition df-padd 30667
 Description: Define projective sum of two subspaces (or more generally two sets of atoms), which is the union of all lines generated by pairs of atoms from each subspace. Lemma 16.2 of [MaedaMaeda] p. 68. For convenience, our definition is generalized to apply to empty sets. (Contributed by NM, 29-Dec-2011.)
Assertion
Ref Expression
df-padd
Distinct variable group:   ,,,,,

Detailed syntax breakdown of Definition df-padd
StepHypRef Expression
1 cpadd 30666 . 2
2 vl . . 3
3 cvv 2958 . . 3
4 vm . . . 4
5 vn . . . 4
62cv 1652 . . . . . 6
7 catm 30135 . . . . . 6
86, 7cfv 5457 . . . . 5
98cpw 3801 . . . 4
104cv 1652 . . . . . 6
115cv 1652 . . . . . 6
1210, 11cun 3320 . . . . 5
13 vp . . . . . . . . . 10
1413cv 1652 . . . . . . . . 9
15 vq . . . . . . . . . . 11
1615cv 1652 . . . . . . . . . 10
17 vr . . . . . . . . . . 11
1817cv 1652 . . . . . . . . . 10
19 cjn 14406 . . . . . . . . . . 11
206, 19cfv 5457 . . . . . . . . . 10
2116, 18, 20co 6084 . . . . . . . . 9
22 cple 13541 . . . . . . . . . 10
236, 22cfv 5457 . . . . . . . . 9
2414, 21, 23wbr 4215 . . . . . . . 8
2524, 17, 11wrex 2708 . . . . . . 7
2625, 15, 10wrex 2708 . . . . . 6
2726, 13, 8crab 2711 . . . . 5
2812, 27cun 3320 . . . 4
294, 5, 9, 9, 28cmpt2 6086 . . 3
302, 3, 29cmpt 4269 . 2
311, 30wceq 1653 1
 Colors of variables: wff set class This definition is referenced by:  paddfval  30668
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