Nuprl Lemma : eu-seg-congruent_wf
∀[e:EuclideanStructure]. ∀[s1,s2:Segment]. (s1 ≡ s2 ∈ ℙ)
Proof
Definitions occuring in Statement :
eu-seg-congruent: s1 ≡ s2,
eu-segment: Segment,
euclidean-structure: EuclideanStructure,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eu-seg-congruent: s1 ≡ s2
Lemmas referenced :
eu-congruent_wf,
eu-seg1_wf,
eu-seg2_wf,
eu-segment_wf,
euclidean-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[e:EuclideanStructure]. \mforall{}[s1,s2:Segment]. (s1 \mequiv{} s2 \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-06_36_40
Last ObjectModification:
2015_12_28-AM-09_25_50
Theory : euclidean!geometry
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