Step
*
of Lemma
oal_neg_eq_nil
∀a:LOSet. ∀b:AbDGrp. ∀ps:|oal(a;b)|. ((--ps) = 00 ∈ |oal(a;b)|
⇐⇒ ps = 00 ∈ |oal(a;b)|)
BY
{ ((Intros THEN (Assert --ps ∈ |oal(a;b)| BY Auto)) THEN Auto) }
1
1. a : LOSet
2. b : AbDGrp
3. ps : |oal(a;b)|
4. --ps ∈ |oal(a;b)|
5. (--ps) = 00 ∈ |oal(a;b)|
⊢ ps = 00 ∈ |oal(a;b)|
2
1. a : LOSet
2. b : AbDGrp
3. ps : |oal(a;b)|
4. --ps ∈ |oal(a;b)|
5. ps = 00 ∈ |oal(a;b)|
⊢ (--ps) = 00 ∈ |oal(a;b)|
Latex:
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDGrp. \mforall{}ps:|oal(a;b)|. ((--ps) = 00 \mLeftarrow{}{}\mRightarrow{} ps = 00)
By
Latex:
((Intros THEN (Assert --ps \mmember{} |oal(a;b)| BY Auto)) THEN Auto)
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