Nuprl Lemma : geo-same-line-reflexive
∀[e:BasicGeometry]. ∀[a,b:Point]. line(a;b)=line(a;b)
Proof
Definitions occuring in Statement :
geo-same-line: line(a;b)=line(c;d),
basic-geometry: BasicGeometry,
geo-point: Point,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
prop: ℙ,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
geo-colinear: Colinear(a;b;c),
and: P ∧ Q,
geo-same-line: line(a;b)=line(c;d),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-point_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-between_wf,
not_wf,
geo-colinear-same
Rules used in proof :
voidElimination,
isect_memberEquality,
independent_isectElimination,
instantiate,
applyEquality,
productEquality,
dependent_functionElimination,
lambdaEquality,
independent_pairEquality,
sqequalRule,
because_Cache,
hypothesis,
productElimination,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
independent_pairFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a,b:Point]. line(a;b)=line(a;b)
Date html generated:
2017_10_02-PM-06_22_58
Last ObjectModification:
2017_08_05-PM-04_17_11
Theory : euclidean!plane!geometry
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