Nuprl Lemma : geo-length-property
∀g:EuclideanPlane. ∀a,b:Point. ab ≅ X|ab|
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-mk-seg: ab,
geo-X: X,
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-point: Point,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
geo-length: |s|,
member: t ∈ T,
top: Top,
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q,
basic-geometry: BasicGeometry,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
sq_stable: SqStable(P),
squash: ↓T,
guard: {T}
Lemmas referenced :
geo_seg1_mk_seg_lemma,
istype-void,
geo_seg2_mk_seg_lemma,
geo-extend_wf,
geo-O_wf,
geo-sep-O-X,
geo-X_wf,
geo-sep_wf,
geo-congruent-iff-length,
sq_stable__geo-congruent,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality_alt,
voidElimination,
hypothesis,
hypothesisEquality,
setElimination,
rename,
because_Cache,
dependent_set_memberEquality_alt,
universeIsType,
isectElimination,
applyEquality,
inhabitedIsType,
productElimination,
independent_isectElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
equalitySymmetry,
equalityIstype,
equalityTransitivity,
instantiate
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b:Point. ab \mcong{} X|ab|
Date html generated:
2019_10_16-PM-01_33_16
Last ObjectModification:
2019_02_18-PM-07_39_45
Theory : euclidean!plane!geometry
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