Nuprl Lemma : not-geo-lt-points
∀g:EuclideanPlane. ∀p,q:{p:Point| B(OXp)} . (¬p < q ⇐⇒ q ≤ p)
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-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
member: t ∈ T,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
rev_implies: P ⇐ Q,
guard: {T},
uimplies: b supposing a,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
squash: ↓T,
exists: ∃x:A. B[x],
l_member: (x ∈ l),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
select: L[n],
cons: [a / b],
cand: A c∧ B,
less_than: a < b,
true: True,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
subtract: n - m,
append: as @ bs,
so_lambda: so_lambda3,
so_apply: x[s1;s2;s3],
geo-colinear-set: geo-colinear-set(e; L),
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
stable: Stable{P},
basic-geometry-: BasicGeometry-,
geo-eq: a ≡ b,
geo-length-type: Length,
quotient: x,y:A//B[x; y]
Latex:
\mforall{}g:EuclideanPlane. \mforall{}p,q:\{p:Point| B(OXp)\} . (\mneg{}p < q \mLeftarrow{}{}\mRightarrow{} q \mleq{} p)
Date html generated:
2020_05_20-AM-10_00_14
Last ObjectModification:
2020_01_13-PM-03_43_19
Theory : euclidean!plane!geometry
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