Nuprl Lemma : trivial-lengths-equal
∀[e:BasicGeometry]. ∀[a,b:Point]. (|aa| = |bb| ∈ Length)
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-point: Point,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
geo-length-type_wf,
trivial-zero-length,
geo-length_wf,
geo-mk-seg_wf,
subtype_rel_self,
iff_weakening_equal,
geo-zero-length_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
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
setElimination,
rename,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
because_Cache,
independent_isectElimination,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a,b:Point]. (|aa| = |bb|)
Date html generated:
2018_05_22-AM-11_55_58
Last ObjectModification:
2018_04_10-PM-04_35_44
Theory : euclidean!plane!geometry
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