Nuprl Lemma : geo-le-pt-reflexivity
∀e:BasicGeometry. ∀a,b:Point. ab≤ab
Proof
Definitions occuring in Statement :
geo-le-pt: ab≤cd,
basic-geometry: BasicGeometry,
geo-point: Point,
all: ∀x:A. B[x]
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
and: P ∧ Q,
member: t ∈ T,
exists: ∃x:A. B[x],
geo-le-pt: ab≤cd,
all: ∀x:A. B[x]
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-congruent_wf,
geo-between_wf,
geo-congruent-refl,
geo-between-trivial
Rules used in proof :
independent_isectElimination,
instantiate,
sqequalRule,
applyEquality,
productEquality,
because_Cache,
independent_pairFormation,
hypothesis,
isectElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
hypothesisEquality,
dependent_pairFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b:Point. ab\mleq{}ab
Date html generated:
2017_10_02-PM-06_46_20
Last ObjectModification:
2017_08_05-PM-04_51_15
Theory : euclidean!plane!geometry
Home
Index