Nuprl Lemma : geo-inner-five-segment
∀e:EuclideanPlane
∀[a,b,c,d,A,B,C,D:Point]. (bd ≅ BD) supposing (cd ≅ CD and ad ≅ AD and bc ≅ BC and ac ≅ AC and B(ABC) and B(abc))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-between: B(abc),
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
euclidean-plane: EuclideanPlane,
stable: Stable{P},
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
geo-congruent: ab ≅ cd,
guard: {T},
or: P ∨ Q,
and: P ∧ Q,
geo-eq: a ≡ b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
basic-geometry-: BasicGeometry-
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,d,A,B,C,D:Point].
(bd \mcong{} BD) supposing (cd \mcong{} CD and ad \mcong{} AD and bc \mcong{} BC and ac \mcong{} AC and B(ABC) and B(abc))
Date html generated:
2020_05_20-AM-09_49_34
Last ObjectModification:
2020_01_27-PM-10_03_31
Theory : euclidean!plane!geometry
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