Nuprl Lemma : geo-inner-three-segment
∀e:EuclideanPlane. ∀[a,b,c,A,B,C:Point]. (ab ≅ AB) supposing (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],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
geo-congruent: ab ≅ cd,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,A,B,C:Point]. (ab \mcong{} AB) supposing (bc \mcong{} BC and ac \mcong{} AC and B(ABC) and B(abc))
Date html generated:
2020_05_20-AM-09_49_41
Last ObjectModification:
2020_01_27-PM-10_03_39
Theory : euclidean!plane!geometry
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