Nuprl Lemma : Euclid-erect-perp-ext
∀e:EuclideanPlane. ∀a:Point. ∀b:{b:Point| a # b} . ∀c:{c:Point| Colinear(a;b;c)} . (∃p:Point [(ab ⊥c pc ∧ p # ab)])
Proof
Definitions occuring in Statement :
geo-perp-in: ab ⊥x cd,
euclidean-plane: EuclideanPlane,
geo-colinear: Colinear(a;b;c),
geo-lsep: a # bc,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
and: P ∧ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
member: t ∈ T,
record-select: r.x,
ifthenelse: if b then t else f fi ,
Euclid-erect-perp,
geo-sep-or,
geo-sep-sym,
symmetric-point-construction,
Euclid-Prop1,
basic-geo-sep-sym,
sq_stable__geo-axioms,
Euclid-Prop1-left-ext,
geo-cong-preserves-gt-prim,
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:Point. \mforall{}b:\{b:Point| a \# b\} . \mforall{}c:\{c:Point| Colinear(a;b;c)\} .
(\mexists{}p:Point [(ab \mbot{}c pc \mwedge{} p \# ab)])
Date html generated:
2020_05_20-AM-10_03_52
Last ObjectModification:
2020_01_27-PM-07_14_43
Theory : euclidean!plane!geometry
Home
Index