Nuprl Lemma : geo-M_wf
∀e:EuclideanPlaneStructure. ∀a:Point. ∀b:{b:Point| a # b} . ∀c:Point. (M(a;b;c) ∈ a # c ∨ b # c)
Proof
Definitions occuring in Statement :
geo-M: M(a;b;c),
euclidean-plane-structure: EuclideanPlaneStructure,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
or: P ∨ Q,
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
geo-M: M(a;b;c),
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,
uall: ∀[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
Latex:
\mforall{}e:EuclideanPlaneStructure. \mforall{}a:Point. \mforall{}b:\{b:Point| a \# b\} . \mforall{}c:Point. (M(a;b;c) \mmember{} a \# c \mvee{} b \# c)
Date html generated:
2020_05_20-AM-09_45_50
Last ObjectModification:
2020_01_29-PM-00_27_13
Theory : euclidean!plane!geometry
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