Description: cdlemg16zz restated for easier studying. TODO: Discard this after everything is figured out. (Contributed by NM, 26-May-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | cdlemg12.l | |- .<_ = ( le ` K ) |
|
| cdlemg12.j | |- .\/ = ( join ` K ) |
||
| cdlemg12.m | |- ./\ = ( meet ` K ) |
||
| cdlemg12.a | |- A = ( Atoms ` K ) |
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| cdlemg12.h | |- H = ( LHyp ` K ) |
||
| cdlemg12.t | |- T = ( ( LTrn ` K ) ` W ) |
||
| cdlemg12b.r | |- R = ( ( trL ` K ) ` W ) |
||
| Assertion | cdlemg25zz | |- ( ( ( K e. HL /\ W e. H ) /\ ( ( P e. A /\ -. P .<_ W ) /\ ( z e. A /\ -. z .<_ W ) /\ F e. T ) /\ ( G e. T /\ -. ( R ` F ) .<_ ( P .\/ z ) /\ -. ( R ` G ) .<_ ( P .\/ z ) ) ) -> ( ( P .\/ ( F ` ( G ` P ) ) ) ./\ W ) = ( ( z .\/ ( F ` ( G ` z ) ) ) ./\ W ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cdlemg12.l | |- .<_ = ( le ` K ) |
|
| 2 | cdlemg12.j | |- .\/ = ( join ` K ) |
|
| 3 | cdlemg12.m | |- ./\ = ( meet ` K ) |
|
| 4 | cdlemg12.a | |- A = ( Atoms ` K ) |
|
| 5 | cdlemg12.h | |- H = ( LHyp ` K ) |
|
| 6 | cdlemg12.t | |- T = ( ( LTrn ` K ) ` W ) |
|
| 7 | cdlemg12b.r | |- R = ( ( trL ` K ) ` W ) |
|
| 8 | 1 2 3 4 5 6 7 | cdlemg16zz | |- ( ( ( K e. HL /\ W e. H ) /\ ( ( P e. A /\ -. P .<_ W ) /\ ( z e. A /\ -. z .<_ W ) /\ F e. T ) /\ ( G e. T /\ -. ( R ` F ) .<_ ( P .\/ z ) /\ -. ( R ` G ) .<_ ( P .\/ z ) ) ) -> ( ( P .\/ ( F ` ( G ` P ) ) ) ./\ W ) = ( ( z .\/ ( F ` ( G ` z ) ) ) ./\ W ) ) |