Metamath Proof Explorer


Theorem diass

Description: The value of the partial isomorphism A is a set of translations, i.e., a set of vectors. (Contributed by NM, 26-Nov-2013)

Ref Expression
Hypotheses diass.b B = Base K
diass.l ˙ = K
diass.h H = LHyp K
diass.t T = LTrn K W
diass.i I = DIsoA K W
Assertion diass K V W H X B X ˙ W I X T

Proof

Step Hyp Ref Expression
1 diass.b B = Base K
2 diass.l ˙ = K
3 diass.h H = LHyp K
4 diass.t T = LTrn K W
5 diass.i I = DIsoA K W
6 eqid trL K W = trL K W
7 1 2 3 4 6 5 diaval K V W H X B X ˙ W I X = f T | trL K W f ˙ X
8 ssrab2 f T | trL K W f ˙ X T
9 7 8 eqsstrdi K V W H X B X ˙ W I X T