Nuprl Lemma : geo-seg-congruent_transitivity
∀e:BasicGeometry
∀[s1,s2,s3:geo-segment(e)].
(geo-seg-congruent(e; s1; s3)) supposing (geo-seg-congruent(e; s1; s2) and geo-seg-congruent(e; s2; s3))
Proof
Definitions occuring in Statement :
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
geo-segment: geo-segment(e),
basic-geometry: BasicGeometry,
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-seg-congruent: geo-seg-congruent(e; s1; s2),
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Latex:
\mforall{}e:BasicGeometry
\mforall{}[s1,s2,s3:geo-segment(e)].
(geo-seg-congruent(e; s1; s3)) supposing
(geo-seg-congruent(e; s1; s2) and
geo-seg-congruent(e; s2; s3))
Date html generated:
2020_05_20-AM-09_49_14
Last ObjectModification:
2019_12_20-PM-07_37_45
Theory : euclidean!plane!geometry
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