Nuprl Lemma : r2-eu_wf
EuclideanPlane(ℝ^2) ∈ EuclideanPlane
Proof
Definitions occuring in Statement :
r2-eu: EuclideanPlane(ℝ^2),
euclidean-plane: EuclideanPlane,
member: t ∈ T
Definitions unfolded in proof :
r2-eu: EuclideanPlane(ℝ^2),
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-gt-prim: ab>cd,
geo-point: Point,
r2-eu-prim: r2-eu-prim(),
mk-eu-prim: mk-eu-prim,
all: ∀x:A. B[x],
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
subtype_rel: A ⊆r B,
prop: ℙ,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q,
false: False,
geo-lsep: a # bc,
geo-left: a leftof bc,
geo-sep: a # b,
geo-between: B(abc),
geo-colinear: Colinear(a;b;c),
geo-congruent: ab ≅ cd,
geo-length-sep: ab # cd),
circle-strict-overlap: StrictOverlap(a;b;c;d),
uimplies: b supposing a
Latex:
EuclideanPlane(\mBbbR{}\^{}2) \mmember{} EuclideanPlane
Date html generated:
2020_05_20-PM-01_10_33
Last ObjectModification:
2020_02_07-PM-04_26_35
Theory : reals!model!euclidean!geometry
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