Nuprl Lemma : geo-CCL-left
∀g:EuclideanPlane. ∀a,b:Point. ∀c:{c:Point| a # c} . ∀d:Point.
((∃p,q:Point. ((ab ≅ ap ∧ cd>cp) ∧ cd ≅ cq ∧ ab>aq)) ⇒ CCL(a;b;c;d) leftof ac)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-CCL: CCL(a;b;c;d),
geo-congruent: ab ≅ cd,
geo-left: a leftof bc,
geo-sep: a # b,
geo-gt-prim: ab>cd,
geo-point: Point,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane,
uimplies: b supposing a,
and: P ∧ Q,
sq_stable: SqStable(P),
exists: ∃x:A. B[x],
squash: ↓T,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b:Point. \mforall{}c:\{c:Point| a \# c\} . \mforall{}d:Point.
((\mexists{}p,q:Point. ((ab \mcong{} ap \mwedge{} cd>cp) \mwedge{} cd \mcong{} cq \mwedge{} ab>aq)) {}\mRightarrow{} CCL(a;b;c;d) leftof ac)
Date html generated:
2020_05_20-AM-09_44_53
Last ObjectModification:
2019_11_13-PM-02_04_12
Theory : euclidean!plane!geometry
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