Nuprl Lemma : geo-seg-congruent-iff-length
∀e:BasicGeometry. ∀[s,t:geo-segment(e)]. uiff(geo-seg-congruent(e; s; t);|s| ≡ |t|)
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
geo-segment: geo-segment(e),
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
geo-congruent: ab ≅ cd,
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
prop: ℙ,
euclidean-plane: EuclideanPlane,
basic-geometry: BasicGeometry,
false: False,
implies: P ⇒ Q,
not: ¬A,
geo-eq: a ≡ b,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
rev_uimplies: rev_uimplies(P;Q),
geo-length: |s|
Latex:
\mforall{}e:BasicGeometry. \mforall{}[s,t:geo-segment(e)]. uiff(geo-seg-congruent(e; s; t);|s| \mequiv{} |t|)
Date html generated:
2020_05_20-AM-09_51_55
Last ObjectModification:
2019_12_20-PM-08_45_38
Theory : euclidean!plane!geometry
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