Description: Part of proof of Lemma E in Crawley p. 113, 2nd paragraph on p. 114. Y represents t_2. In their notation, we prove t \/ t_2 = t \/ r. (Contributed by NM, 8-Oct-2012) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | cdleme10t.l | |- .<_ = ( le ` K ) |
|
| cdleme10t.j | |- .\/ = ( join ` K ) |
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| cdleme10t.m | |- ./\ = ( meet ` K ) |
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| cdleme10t.a | |- A = ( Atoms ` K ) |
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| cdleme10t.h | |- H = ( LHyp ` K ) |
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| cdleme10t.y | |- Y = ( ( R .\/ T ) ./\ W ) |
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| Assertion | cdleme10tN | |- ( ( ( K e. HL /\ W e. H ) /\ R e. A /\ ( T e. A /\ -. T .<_ W ) ) -> ( T .\/ Y ) = ( T .\/ R ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cdleme10t.l | |- .<_ = ( le ` K ) |
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| 2 | cdleme10t.j | |- .\/ = ( join ` K ) |
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| 3 | cdleme10t.m | |- ./\ = ( meet ` K ) |
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| 4 | cdleme10t.a | |- A = ( Atoms ` K ) |
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| 5 | cdleme10t.h | |- H = ( LHyp ` K ) |
|
| 6 | cdleme10t.y | |- Y = ( ( R .\/ T ) ./\ W ) |
|
| 7 | 1 2 3 4 5 6 | cdleme10 | |- ( ( ( K e. HL /\ W e. H ) /\ R e. A /\ ( T e. A /\ -. T .<_ W ) ) -> ( T .\/ Y ) = ( T .\/ R ) ) |