Nuprl Lemma : geo-length-flip-eq
∀e:BasicGeometry. ∀[a,b:Point]. |ab| ≡ |ba|
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],
all: ∀x:A. B[x]
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
geo-eq: a ≡ b,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
euclidean-plane: EuclideanPlane,
basic-geometry: BasicGeometry,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-point_wf,
geo-congruent-flip-seg,
geo-mk-seg_wf,
geo-seg-congruent-iff-length
Rules used in proof :
instantiate,
applyEquality,
universeIsType,
isectIsTypeImplies,
voidElimination,
isect_memberEquality_alt,
inhabitedIsType,
functionIsTypeImplies,
lambdaEquality_alt,
sqequalRule,
independent_isectElimination,
productElimination,
hypothesisEquality,
hypothesis,
rename,
setElimination,
isectElimination,
because_Cache,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation_alt,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}[a,b:Point]. |ab| \mequiv{} |ba|
Date html generated:
2019_10_29-AM-09_13_36
Last ObjectModification:
2019_10_18-PM-03_17_53
Theory : euclidean!plane!geometry
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