Nuprl Lemma : geo-incident-not-plsep
∀[e:EuclideanPlane]. ∀[x:Point]. ∀[m:Line]. ¬x # m supposing x I m
Proof
Definitions occuring in Statement :
geo-plsep: p # l,
geo-incident: p I L,
geo-line: Line,
euclidean-plane: EuclideanPlane,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
geo-line: Line,
pi1: fst(t),
pi2: snd(t),
geo-plsep: p # l,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
geo-plsep_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-incident_wf,
geoline-subtype1,
geo-line_wf,
geo-point_wf,
geo-incident-line,
geo-lsep_wf,
not-lsep-iff-colinear
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairFormation
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[x:Point]. \mforall{}[m:Line]. \mneg{}x \# m supposing x I m
Date html generated:
2018_05_22-PM-01_07_19
Last ObjectModification:
2018_05_19-PM-08_22_46
Theory : euclidean!plane!geometry
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