Nuprl Lemma : unique-angles-in-half-plane-better
∀e:EuclideanPlane. ∀a,b,c,q:Point. (a leftof bc ⇒ q leftof bc ⇒ qbc ≅a abc ⇒ out(b aq))
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
geo-cong-angle: abc ≅a xyz,
euclidean-plane: EuclideanPlane,
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
guard: {T},
and: P ∧ Q,
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
uiff: uiff(P;Q),
basic-geometry-: BasicGeometry-,
oriented-plane: OrientedPlane,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,q:Point. (a leftof bc {}\mRightarrow{} q leftof bc {}\mRightarrow{} qbc \mcong{}\msuba{} abc {}\mRightarrow{} out(b aq))
Date html generated:
2020_05_20-AM-10_07_03
Last ObjectModification:
2020_01_13-PM-04_02_27
Theory : euclidean!plane!geometry
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