Nuprl Lemma : geo-CC-2
∀g:EuclideanPlane. ∀a,b,c,d:Point.
(a # c
⇒ (∃p,q:Point. ((ab ≅ ap ∧ cd>cp) ∧ cd ≅ cq ∧ ab>aq))
⇒ (∃z1,z2:Point. (az1 ≅ ab ∧ az2 ≅ ab ∧ cz1 ≅ cd ∧ cz2 ≅ cd ∧ z1 leftof ac ∧ z2 leftof ca)))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
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
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
cand: A c∧ B,
guard: {T},
uimplies: b supposing a,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
squash: ↓T
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c,d:Point.
(a \# c
{}\mRightarrow{} (\mexists{}p,q:Point. ((ab \mcong{} ap \mwedge{} cd>cp) \mwedge{} cd \mcong{} cq \mwedge{} ab>aq))
{}\mRightarrow{} (\mexists{}z1,z2:Point. (az1 \mcong{} ab \mwedge{} az2 \mcong{} ab \mwedge{} cz1 \mcong{} cd \mwedge{} cz2 \mcong{} cd \mwedge{} z1 leftof ac \mwedge{} z2 leftof ca)))
Date html generated:
2020_05_20-AM-09_47_04
Last ObjectModification:
2019_11_13-PM-02_26_45
Theory : euclidean!plane!geometry
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