Description: A lattice dilation is a one-to-one onto function. (Contributed by NM, 19-Apr-2013)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ldil1o.b | |- B = ( Base ` K ) |
|
ldil1o.h | |- H = ( LHyp ` K ) |
||
ldil1o.d | |- D = ( ( LDil ` K ) ` W ) |
||
Assertion | ldil1o | |- ( ( ( K e. V /\ W e. H ) /\ F e. D ) -> F : B -1-1-onto-> B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ldil1o.b | |- B = ( Base ` K ) |
|
2 | ldil1o.h | |- H = ( LHyp ` K ) |
|
3 | ldil1o.d | |- D = ( ( LDil ` K ) ` W ) |
|
4 | simpll | |- ( ( ( K e. V /\ W e. H ) /\ F e. D ) -> K e. V ) |
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5 | eqid | |- ( LAut ` K ) = ( LAut ` K ) |
|
6 | 2 5 3 | ldillaut | |- ( ( ( K e. V /\ W e. H ) /\ F e. D ) -> F e. ( LAut ` K ) ) |
7 | 1 5 | laut1o | |- ( ( K e. V /\ F e. ( LAut ` K ) ) -> F : B -1-1-onto-> B ) |
8 | 4 6 7 | syl2anc | |- ( ( ( K e. V /\ W e. H ) /\ F e. D ) -> F : B -1-1-onto-> B ) |