Nuprl Lemma : geo-opp-side-trivial
∀[e:BasicGeometry]. ∀[A,P,Q:Point]. (¬P-AA-Q)
Proof
Definitions occuring in Statement :
geo-opp-side: P-AB-Q,
basic-geometry: BasicGeometry,
geo-point: Point,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
implies: P ⇒ Q,
not: ¬A,
member: t ∈ T,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
geo-opp-side: P-AB-Q
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
geo-opp-side_wf,
geo-colinear-same
Rules used in proof :
isect_memberEquality,
independent_isectElimination,
instantiate,
applyEquality,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
hypothesisEquality,
isectElimination,
extract_by_obid,
voidElimination,
independent_functionElimination,
sqequalHypSubstitution,
hypothesis,
because_Cache,
thin,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
productElimination
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[A,P,Q:Point]. (\mneg{}P-AA-Q)
Date html generated:
2017_10_02-PM-06_21_34
Last ObjectModification:
2017_08_05-PM-04_16_04
Theory : euclidean!plane!geometry
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