Step
*
of Lemma
cons_in_oalist
∀a:LOSet. ∀b:AbDMon. ∀ws:|oal(a;b)|. ∀x:|a|. ∀y:|b|.
((↑before(x;map(λx.(fst(x));ws)))
⇒ (¬(y = e ∈ |b|))
⇒ ([<x, y> / ws] ∈ |oal(a;b)|))
BY
{ ((RepD) THENA Auto) }
1
1. a : LOSet
2. b : AbDMon
3. ws : |oal(a;b)|
4. x : |a|
5. y : |b|
6. ↑before(x;map(λx.(fst(x));ws))
7. ¬(y = e ∈ |b|)
⊢ [<x, y> / ws] ∈ |oal(a;b)|
Latex:
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. \mforall{}ws:|oal(a;b)|. \mforall{}x:|a|. \mforall{}y:|b|.
((\muparrow{}before(x;map(\mlambda{}x.(fst(x));ws))) {}\mRightarrow{} (\mneg{}(y = e)) {}\mRightarrow{} ([<x, y> / ws] \mmember{} |oal(a;b)|))
By
Latex:
((RepD) THENA Auto)
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