Description: cdlemg16zz restated for easier studying. TODO: Discard this after everything is figured out. (Contributed by NM, 26-May-2013)
Ref | Expression | ||
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Hypotheses | cdlemg12.l | |- .<_ = ( le ` K ) |
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cdlemg12.j | |- .\/ = ( join ` K ) |
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cdlemg12.m | |- ./\ = ( meet ` K ) |
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cdlemg12.a | |- A = ( Atoms ` K ) |
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cdlemg12.h | |- H = ( LHyp ` K ) |
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cdlemg12.t | |- T = ( ( LTrn ` K ) ` W ) |
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cdlemg12b.r | |- R = ( ( trL ` K ) ` W ) |
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Assertion | cdlemg26zz | |- ( ( ( K e. HL /\ W e. H ) /\ ( ( Q e. A /\ -. Q .<_ W ) /\ ( z e. A /\ -. z .<_ W ) /\ F e. T ) /\ ( G e. T /\ -. ( R ` F ) .<_ ( Q .\/ z ) /\ -. ( R ` G ) .<_ ( Q .\/ z ) ) ) -> ( ( Q .\/ ( F ` ( G ` Q ) ) ) ./\ W ) = ( ( z .\/ ( F ` ( G ` z ) ) ) ./\ W ) ) |
Step | Hyp | Ref | Expression |
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1 | cdlemg12.l | |- .<_ = ( le ` K ) |
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2 | cdlemg12.j | |- .\/ = ( join ` K ) |
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3 | cdlemg12.m | |- ./\ = ( meet ` K ) |
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4 | cdlemg12.a | |- A = ( Atoms ` K ) |
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5 | cdlemg12.h | |- H = ( LHyp ` K ) |
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6 | cdlemg12.t | |- T = ( ( LTrn ` K ) ` W ) |
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7 | cdlemg12b.r | |- R = ( ( trL ` K ) ` W ) |
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8 | 1 2 3 4 5 6 7 | cdlemg25zz | |- ( ( ( K e. HL /\ W e. H ) /\ ( ( Q e. A /\ -. Q .<_ W ) /\ ( z e. A /\ -. z .<_ W ) /\ F e. T ) /\ ( G e. T /\ -. ( R ` F ) .<_ ( Q .\/ z ) /\ -. ( R ` G ) .<_ ( Q .\/ z ) ) ) -> ( ( Q .\/ ( F ` ( G ` Q ) ) ) ./\ W ) = ( ( z .\/ ( F ` ( G ` z ) ) ) ./\ W ) ) |