Nuprl Lemma : geo-midpoint-diagonals-congruent
∀e:BasicGeometry. ∀A,P,Q,p,q:Point. (p=A=P ⇒ q=A=Q ⇒ PQ ≅ pq)
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-midpoint: a=m=b,
geo-congruent: ab ≅ cd,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
geo-midpoint: a=m=b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
or: P ∨ Q,
not: ¬A,
false: False,
stable: Stable{P},
geo-eq: a ≡ b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
exists: ∃x:A. B[x],
basic-geometry-: BasicGeometry-,
squash: ↓T,
true: True,
cand: A c∧ B
Latex:
\mforall{}e:BasicGeometry. \mforall{}A,P,Q,p,q:Point. (p=A=P {}\mRightarrow{} q=A=Q {}\mRightarrow{} PQ \mcong{} pq)
Date html generated:
2020_05_20-AM-09_57_18
Last ObjectModification:
2020_01_27-PM-10_01_02
Theory : euclidean!plane!geometry
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