Nuprl Lemma : lsep-inner-pasch
∀e:OrientedPlane. ∀a,b:Point. ∀c:{c:Point| c # ab} . ∀p:{p:Point| a-p-c} . ∀q:{q:Point| b-q-c} .
(∃x:Point [(B(bxp) ∧ B(axq))])
Proof
Definitions occuring in Statement :
oriented-plane: OrientedPlane,
geo-strict-between: a-b-c,
geo-between: B(abc),
geo-lsep: a # bc,
geo-point: Point,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
and: P ∧ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
oriented-plane: OrientedPlane,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
or: P ∨ Q,
and: P ∧ Q,
cand: A c∧ B,
basic-geometry-: BasicGeometry-,
exists: ∃x:A. B[x],
sq_exists: ∃x:A [B[x]],
geo-eq: a ≡ b,
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
cons: [a / b],
select: L[n],
satisfiable_int_formula: satisfiable_int_formula(fmla),
decidable: Dec(P),
lelt: i ≤ j < k,
int_seg: {i..j-},
l_all: (∀x∈L.P[x]),
geo-colinear-set: geo-colinear-set(e; L),
geo-lsep: a # bc
Latex:
\mforall{}e:OrientedPlane. \mforall{}a,b:Point. \mforall{}c:\{c:Point| c \# ab\} . \mforall{}p:\{p:Point| a-p-c\} . \mforall{}q:\{q:Point| b-q-c\} .
(\mexists{}x:Point [(B(bxp) \mwedge{} B(axq))])
Date html generated:
2020_05_20-AM-09_50_27
Last ObjectModification:
2020_01_13-PM-03_25_20
Theory : euclidean!plane!geometry
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