Nuprl Lemma : Euclid-Prop7
∀e:EuclideanPlane. ∀a,b:Point. ∀c,d:{p:Point| p leftof ab} . (ac ≅ ad ⇒ bc ≅ bd ⇒ c ≡ d)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-eq: a ≡ b,
geo-congruent: ab ≅ cd,
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-eq: a ≡ b,
not: ¬A,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
sq_exists: ∃x:A [B[x]],
false: False,
geo-midpoint: a=m=b,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
basic-geometry: BasicGeometry,
uiff: uiff(P;Q),
oriented-plane: OrientedPlane,
geo-colinear: Colinear(a;b;c),
cand: A c∧ B
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b:Point. \mforall{}c,d:\{p:Point| p leftof ab\} . (ac \mcong{} ad {}\mRightarrow{} bc \mcong{} bd {}\mRightarrow{} c \mequiv{} d)
Date html generated:
2020_05_20-AM-10_05_21
Last ObjectModification:
2019_12_03-AM-09_52_29
Theory : euclidean!plane!geometry
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