Nuprl Lemma : geo-Op-sep
∀g:EuclideanPlane. ∀p:{p:Point| O_X_p} . O ≠ p
Proof
Definitions occuring in Statement :
geo-X: X,
geo-O: O,
euclidean-plane: EuclideanPlane,
geo-between: a_b_c,
geo-sep: a ≠ b,
geo-point: Point,
all: ∀x:A. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T,
implies: P ⇒ Q,
sq_stable: SqStable(P),
euclidean-plane: EuclideanPlane,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
geo-between_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-point_wf,
set_wf,
geo-sep-O-X,
geo-X_wf,
geo-between-sep,
geo-O_wf,
sq_stable__geo-sep
Rules used in proof :
lambdaEquality,
independent_isectElimination,
instantiate,
applyEquality,
isectElimination,
imageElimination,
baseClosed,
imageMemberEquality,
sqequalRule,
independent_functionElimination,
hypothesisEquality,
hypothesis,
because_Cache,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
rename,
thin,
setElimination,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlane. \mforall{}p:\{p:Point| O\_X\_p\} . O \mneq{} p
Date html generated:
2017_10_02-PM-03_29_05
Last ObjectModification:
2017_08_04-PM-09_35_35
Theory : euclidean!plane!geometry
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