Description: Part of proof of Lemma E in Crawley p. 113, 2nd paragraph on p. 114. X represents t_1. In their notation, we prove p \/ t_1 = p \/ t. (Contributed by NM, 8-Oct-2012) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | cdleme8t.l | |- .<_ = ( le ` K ) |
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| cdleme8t.j | |- .\/ = ( join ` K ) |
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| cdleme8t.m | |- ./\ = ( meet ` K ) |
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| cdleme8t.a | |- A = ( Atoms ` K ) |
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| cdleme8t.h | |- H = ( LHyp ` K ) |
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| cdleme8t.x | |- X = ( ( P .\/ T ) ./\ W ) |
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| Assertion | cdleme8tN | |- ( ( ( K e. HL /\ W e. H ) /\ ( P e. A /\ -. P .<_ W ) /\ T e. A ) -> ( P .\/ X ) = ( P .\/ T ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cdleme8t.l | |- .<_ = ( le ` K ) |
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| 2 | cdleme8t.j | |- .\/ = ( join ` K ) |
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| 3 | cdleme8t.m | |- ./\ = ( meet ` K ) |
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| 4 | cdleme8t.a | |- A = ( Atoms ` K ) |
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| 5 | cdleme8t.h | |- H = ( LHyp ` K ) |
|
| 6 | cdleme8t.x | |- X = ( ( P .\/ T ) ./\ W ) |
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| 7 | 1 2 3 4 5 6 | cdleme8 | |- ( ( ( K e. HL /\ W e. H ) /\ ( P e. A /\ -. P .<_ W ) /\ T e. A ) -> ( P .\/ X ) = ( P .\/ T ) ) |