Nuprl Lemma : geo-CC_wf
∀[g:EuclideanPlaneStructure]. ∀[a,b:Point]. ∀[c:{c:Point| a # c} ]. ∀[d:{d:Point| StrictOverlap(a;b;c;d)} ].
(CC(a;b;c;d) ∈ {u:Point| ab ≅ au ∧ cd ≅ cu ∧ u leftof ac} )
Proof
Definitions occuring in Statement :
geo-CC: CC(a;b;c;d),
euclidean-plane-structure: EuclideanPlaneStructure,
circle-strict-overlap: StrictOverlap(a;b;c;d),
geo-congruent: ab ≅ cd,
geo-left: a leftof bc,
geo-sep: a # b,
geo-point: Point,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
euclidean-plane-structure: EuclideanPlaneStructure,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
all: ∀x:A. B[x],
prop: ℙ,
or: P ∨ Q,
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_exists: ∃x:A [B[x]],
and: P ∧ Q,
implies: P ⇒ Q,
geo-CC: CC(a;b;c;d)
Latex:
\mforall{}[g:EuclideanPlaneStructure]. \mforall{}[a,b:Point]. \mforall{}[c:\{c:Point| a \# c\} ]. \mforall{}[d:\{d:Point|
StrictOverlap(a;b;c;d)\} ].
(CC(a;b;c;d) \mmember{} \{u:Point| ab \mcong{} au \mwedge{} cd \mcong{} cu \mwedge{} u leftof ac\} )
Date html generated:
2020_05_20-AM-09_43_39
Last ObjectModification:
2019_12_03-AM-09_53_19
Theory : euclidean!plane!geometry
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