Nuprl Lemma : geo-CCR_wf
∀[g:EuclideanPlaneStructure]
∀a,b:Point. ∀c:{c:Point| c # a} . ∀d:Point.
geo-CCR(g;a;b;c;d) ∈ {v:Point| ab ≅ av ∧ cd ≅ cv ∧ v leftof ca} supposing ∃p,q:Point. ((ab ≅ ap ∧ cd>cp) ∧ cd ≅ cq \000C∧ ab>aq)
Proof
Definitions occuring in Statement :
geo-CCR: geo-CCR(g;a;b;c;d),
euclidean-plane-structure: EuclideanPlaneStructure,
geo-congruent: ab ≅ cd,
geo-left: a leftof bc,
geo-sep: a # b,
geo-gt-prim: ab>cd,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
geo-CCR: geo-CCR(g;a;b;c;d),
exists: ∃x:A. B[x],
and: P ∧ Q,
circle-strict-overlap: StrictOverlap(a;b;c;d),
cand: A c∧ B,
subtype_rel: A ⊆r B,
prop: ℙ,
squash: ↓T
Latex:
\mforall{}[g:EuclideanPlaneStructure]
\mforall{}a,b:Point. \mforall{}c:\{c:Point| c \# a\} . \mforall{}d:Point.
geo-CCR(g;a;b;c;d) \mmember{} \{v:Point| ab \mcong{} av \mwedge{} cd \mcong{} cv \mwedge{} v leftof ca\}
supposing \mexists{}p,q:Point. ((ab \mcong{} ap \mwedge{} cd>cp) \mwedge{} cd \mcong{} cq \mwedge{} ab>aq)
Date html generated:
2020_05_20-AM-09_43_55
Last ObjectModification:
2019_11_13-PM-02_05_33
Theory : euclidean!plane!geometry
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