Changes

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<math>\begin{array}{lll}

<math>\begin{array}{lll}

u \cdot L

u \star L

& = &

& = &

L_{u \,\text{at}\, 1}

L_{u \,\text{at}\, 1}

\text{the set of ordered pairs in}~ L ~\text{that have}~ u ~\text{in the 1st place}.

\text{the set of ordered pairs in}~ L ~\text{that have}~ u ~\text{in the 1st place}.

\\[9pt]

\\[9pt]

L \cdot v

L \star v

& = &

& = &

L_{v \,\text{at}\, 2}

L_{v \,\text{at}\, 2}

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The denotation of the term <math>\mathit{l}^\mathrm{w}\!</math> is a subset of <math>X\!</math> that can be obtained as follows:  Consider the flags of the form <math>L \cdot x</math> for each <math>x \in W,</math> take their intersection <math>\textstyle\bigcap_{x \in W} L \cdot x,</math> and collect the elements of <math>X\!</math> that appear as the first components of these ordered pairs.  Putting it all together:

The denotation of the term <math>\mathit{l}^\mathrm{w}\!</math> is a subset of <math>X\!</math> that can be obtained as follows:  Consider the flags of the form <math>L \star x</math> for each <math>x \in W,</math> take their intersection <math>\textstyle\bigcap_{x \in W} L \star x,</math> and collect the elements of <math>X\!</math> that appear as the first components of these ordered pairs.  Putting it all together:

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" width="90%"

| <math>\mathit{l}^\mathrm{w} ~=~ \operatorname{proj}_1 \bigcap_{x \in W} L \cdot x</math>

| <math>\mathit{l}^\mathrm{w} ~=~ \operatorname{proj}_1 \bigcap_{x \in W} L \star x</math>

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