Nuprl Lemma : Euclid-Prop5_1-not-tri
∀e:EuclideanPlane. ∀a,b,c:Point. (b # c ⇒ ab ≅ ac ⇒ abc ≅a acb)
Proof
Definitions occuring in Statement :
geo-cong-angle: abc ≅a xyz,
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-cong-angle: abc ≅a xyz,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
basic-geometry: BasicGeometry,
uiff: uiff(P;Q),
exists: ∃x:A. B[x],
or: P ∨ Q,
euclidean-plane: EuclideanPlane
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c:Point. (b \# c {}\mRightarrow{} ab \mcong{} ac {}\mRightarrow{} abc \mcong{}\msuba{} acb)
Date html generated:
2020_05_20-AM-10_03_41
Last ObjectModification:
2020_01_27-PM-10_00_21
Theory : euclidean!plane!geometry
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