Step
*
2
of Lemma
distinct_iff_counts_le_one
1. s : DSet
2. p : |s|
3. ps : |s| List
4. ↑distinct{s}(ps)
⇐⇒ ∀x:|s|. ((x #∈ ps) ≤ 1)
⊢ ↑((∀br(:|s|) ∈ ps. (¬b(r (=b) p))) ∧b distinct{s}(ps))
⇐⇒ ∀x:|s|. ((b2i(p (=b) x) + (x #∈ ps)) ≤ 1)
BY
{ (RewriteWith [] ``ball_char assert_of_band assert_of_bnot assert_of_dset_eq`` 0 THENA Auto) }
1
1. s : DSet
2. p : |s|
3. ps : |s| List
4. ↑distinct{s}(ps)
⇐⇒ ∀x:|s|. ((x #∈ ps) ≤ 1)
⊢ (∀r:|s|. ((↑(r ∈b ps))
⇒ (¬(r = p ∈ |s|)))) ∧ (↑distinct{s}(ps))
⇐⇒ ∀x:|s|. ((b2i(p (=b) x) + (x #∈ ps)) ≤ 1)
Latex:
Latex:
1. s : DSet
2. p : |s|
3. ps : |s| List
4. \muparrow{}distinct\{s\}(ps) \mLeftarrow{}{}\mRightarrow{} \mforall{}x:|s|. ((x \#\mmember{} ps) \mleq{} 1)
\mvdash{} \muparrow{}((\mforall{}\msubb{}r(:|s|) \mmember{} ps. (\mneg{}\msubb{}(r (=\msubb{}) p))) \mwedge{}\msubb{} distinct\{s\}(ps))
\mLeftarrow{}{}\mRightarrow{} \mforall{}x:|s|. ((b2i(p (=\msubb{}) x) + (x \#\mmember{} ps)) \mleq{} 1)
By
Latex:
(RewriteWith [] ``ball\_char assert\_of\_band assert\_of\_bnot assert\_of\_dset\_eq`` 0 THENA Auto)
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