Nuprl Lemma : geo-seg-congruent_wf
∀[e:EuclideanPlaneStructure]. ∀[s1,s2:geo-segment(e)]. (geo-seg-congruent(e; s1; s2) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
geo-segment: geo-segment(e),
euclidean-plane-structure: EuclideanPlaneStructure,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
geo-segment_wf,
geo-seg2_wf,
geo-seg1_wf,
euclidean-plane-structure-subtype,
geo-congruent_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:EuclideanPlaneStructure]. \mforall{}[s1,s2:geo-segment(e)]. (geo-seg-congruent(e; s1; s2) \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-04_44_50
Last ObjectModification:
2017_08_05-AM-09_28_05
Theory : euclidean!plane!geometry
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