Nuprl Lemma : Euclid-Prop2-ext
∀e:EuclideanPlane. ∀a,b,c:Point. (∃x:Point [ax ≅ bc])
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-point: Point,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]]
Definitions unfolded in proof :
member: t ∈ T,
record-select: r.x,
ifthenelse: if b then t else f fi ,
Euclid-Prop2,
geo-sep-exists,
geo-sep-or,
Euclid-Prop2-lemma-ext,
geo-sep-sym,
basic-geo-sep-sym,
sq_stable__geo-axioms,
sq_stable-geo-axioms-if,
sq_stable__geo-between,
sq_stable__geo-congruent,
sq_stable__geo-gt-prim,
sq_stable__geo-lsep,
any: any x,
sq_stable__and,
sq_stable__all,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda4,
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c:Point. (\mexists{}x:Point [ax \mcong{} bc])
Date html generated:
2020_05_20-AM-09_51_13
Last ObjectModification:
2020_01_27-PM-07_08_35
Theory : euclidean!plane!geometry
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