Nuprl Lemma : Euclid-Prop1-left
∀e:EuclideanPlane. ∀a:Point. ∀b:{b:Point| a # b} . (∃c:Point [(((cb ≅ ab ∧ ca ≅ ba) ∧ ca ≅ cb) ∧ c leftof ab)])
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-left: a leftof bc,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
and: P ∧ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
squash: ↓T,
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
geo-sep: a # b,
record-select: r.x,
geo-gt-prim: ab>cd,
cand: A c∧ B,
and: P ∧ Q,
sq_exists: ∃x:A [B[x]]
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a:Point. \mforall{}b:\{b:Point| a \# b\} .
(\mexists{}c:Point [(((cb \mcong{} ab \mwedge{} ca \mcong{} ba) \mwedge{} ca \mcong{} cb) \mwedge{} c leftof ab)])
Date html generated:
2020_05_20-AM-09_47_14
Last ObjectModification:
2020_01_27-PM-10_03_51
Theory : euclidean!plane!geometry
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