Nuprl Lemma : geo-extend-equal-iff-congruent
∀e:BasicGeometry. ∀[a,b,c,d,c',d':Point]. uiff(extend ab by cd ≡ extend ab by c'd';cd ≅ c'd') supposing a # b
Proof
Definitions occuring in Statement :
geo-extend: extend qa by bc,
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-congruent: ab ≅ cd,
geo-sep: a # b,
geo-point: Point,
uiff: uiff(P;Q),
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,
subtype_rel: A ⊆r B,
prop: ℙ,
basic-geometry: BasicGeometry,
implies: P ⇒ Q,
and: P ∧ Q,
uiff: uiff(P;Q),
geo-congruent: ab ≅ cd,
not: ¬A,
false: False,
geo-eq: a ≡ b,
guard: {T},
iff: P ⇐⇒ Q,
cand: A c∧ B
Latex:
\mforall{}e:BasicGeometry
\mforall{}[a,b,c,d,c',d':Point]. uiff(extend ab by cd \mequiv{} extend ab by c'd';cd \mcong{} c'd') supposing a \# b
Date html generated:
2020_05_20-AM-09_51_27
Last ObjectModification:
2019_12_20-PM-08_45_44
Theory : euclidean!plane!geometry
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