Nuprl Lemma : length-seg-eq
∀[e:BasicGeometry]. ∀[a,b:Point]. |ab| ≡ |ab|
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-point: Point,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
prop: ℙ,
geo-eq: a ≡ b,
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
geo-eq_weakening,
geo-length_wf1,
geo-mk-seg_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
basic-geometry_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-between_wf,
geo-O_wf,
geo-X_wf,
geo-sep_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
hypothesis,
applyEquality,
lambdaEquality,
setEquality,
instantiate,
independent_isectElimination,
sqequalRule,
because_Cache,
dependent_functionElimination,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a,b:Point]. |ab| \mequiv{} |ab|
Date html generated:
2018_05_22-AM-11_55_47
Last ObjectModification:
2018_04_10-PM-04_29_55
Theory : euclidean!plane!geometry
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