Nuprl Lemma : geo-lt-iff-strict-between-points
∀g:EuclideanPlane. ∀p,q:{p:Point| B(OXp)} . (p < q ⇐⇒ p ≤ q ∧ p # q)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-le: p ≤ q,
geo-X: X,
geo-O: O,
euclidean-plane: EuclideanPlane,
geo-between: B(abc),
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
euclidean-plane: EuclideanPlane,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
basic-geometry: BasicGeometry,
rev_implies: P ⇐ Q,
cand: A c∧ B,
geo-lt: p < q,
exists: ∃x:A. B[x],
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
geo-length-type: Length,
geo_ge: geo_ge(e; p; q),
squash: ↓T,
geo-le: p ≤ q,
sq_stable: SqStable(P),
false: False,
quotient: x,y:A//B[x; y],
not: ¬A,
geo-eq: a ≡ b
Latex:
\mforall{}g:EuclideanPlane. \mforall{}p,q:\{p:Point| B(OXp)\} . (p < q \mLeftarrow{}{}\mRightarrow{} p \mleq{} q \mwedge{} p \# q)
Date html generated:
2020_05_20-AM-09_59_48
Last ObjectModification:
2020_01_13-PM-03_43_38
Theory : euclidean!plane!geometry
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