Nuprl Lemma : geo-midpoint-trivial
∀e:BasicGeometry. ∀a:Point. a=a=a
Proof
Definitions occuring in Statement :
geo-midpoint: a=m=b,
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,
uall: ∀[x:A]. B[x],
member: t ∈ T,
cand: A c∧ B,
and: P ∧ Q,
all: ∀x:A. B[x],
geo-midpoint: a=m=b
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-refl,
geo-between-trivial
Rules used in proof :
independent_isectElimination,
instantiate,
applyEquality,
independent_pairFormation,
hypothesis,
because_Cache,
isectElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a:Point. a=a=a
Date html generated:
2017_10_02-PM-04_46_00
Last ObjectModification:
2017_08_05-AM-11_46_01
Theory : euclidean!plane!geometry
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