Nuprl Lemma : geo-cong-angle-transitivity
∀e:BasicGeometry. ∀a,b,c,x,y,z,p,q,r:Point. (abc ≅a xyz ⇒ xyz ≅a pqr ⇒ abc ≅a pqr)
Proof
Definitions occuring in Statement :
geo-cong-angle: abc ≅a xyz,
basic-geometry: BasicGeometry,
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,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
exists: ∃x:A. B[x],
euclidean-plane: EuclideanPlane,
basic-geometry-: BasicGeometry-,
uiff: uiff(P;Q),
squash: ↓T,
true: True
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,x,y,z,p,q,r:Point. (abc \mcong{}\msuba{} xyz {}\mRightarrow{} xyz \mcong{}\msuba{} pqr {}\mRightarrow{} abc \mcong{}\msuba{} pqr)
Date html generated:
2020_05_20-AM-09_56_49
Last ObjectModification:
2020_01_14-AM-10_24_06
Theory : euclidean!plane!geometry
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