Nuprl Lemma : geo-CCL_wf
∀[g:EuclideanPlaneStructure]
(BasicGeometryAxioms(g)
⇒ (∀a,b:Point. ∀c:{c:Point| a # c} . ∀d:Point.
CCL(a;b;c;d) ∈ {u:Point| ab ≅ au ∧ cd ≅ cu ∧ u leftof ac} supposing ∃p,q:Point. ((ab ≅ ap ∧ cd>cp) ∧ cd ≅ cq ∧ \000Cab>aq)))
Proof
Definitions occuring in Statement :
geo-CCL: CCL(a;b;c;d),
euclidean-plane-structure: EuclideanPlaneStructure,
basic-geo-axioms: BasicGeometryAxioms(g),
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],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
circle-strict-overlap: StrictOverlap(a;b;c;d),
squash: ↓T,
subtype_rel: A ⊆r B,
geo-CCL: CCL(a;b;c;d),
guard: {T},
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q
Latex:
\mforall{}[g:EuclideanPlaneStructure]
(BasicGeometryAxioms(g)
{}\mRightarrow{} (\mforall{}a,b:Point. \mforall{}c:\{c:Point| a \# c\} . \mforall{}d:Point.
CCL(a;b;c;d) \mmember{} \{u:Point| ab \mcong{} au \mwedge{} cd \mcong{} cu \mwedge{} u leftof ac\}
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_50
Last ObjectModification:
2019_11_13-PM-02_16_16
Theory : euclidean!plane!geometry
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