Nuprl Lemma : geo-five-segment
∀e:EuclideanPlane
∀[a,b,c,d,A,B,C,D:Point].
(cd ≅ CD) supposing (bd ≅ BD and ad ≅ AD and bc ≅ BC and ab ≅ AB and B(ABC) and B(abc) and a # b)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-between: B(abc),
geo-sep: a # b,
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],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
implies: P ⇒ Q,
geo-congruent: ab ≅ cd,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,d,A,B,C,D:Point].
(cd \mcong{} CD) supposing
(bd \mcong{} BD and
ad \mcong{} AD and
bc \mcong{} BC and
ab \mcong{} AB and
B(ABC) and
B(abc) and
a \# b)
Date html generated:
2020_05_20-AM-09_46_50
Last ObjectModification:
2019_11_13-PM-01_56_22
Theory : euclidean!plane!geometry
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