Nuprl Lemma : geo-three-segment
∀e:EuclideanPlane. ∀[a,b,c,A,B,C:Point]. (ac ≅ AC) supposing (bc ≅ BC and ab ≅ AB 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,
geo-congruent: ab ≅ cd,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
euclidean-plane: EuclideanPlane,
or: P ∨ Q,
stable: Stable{P},
geo-eq: a ≡ b,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,A,B,C:Point]. (ac \mcong{} AC) supposing (bc \mcong{} BC and ab \mcong{} AB and B(ABC) and B(abc))
Date html generated:
2020_05_20-AM-09_50_46
Last ObjectModification:
2019_12_20-PM-08_45_55
Theory : euclidean!plane!geometry
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