Nuprl Lemma : eu-seg-congruent_transitivity
∀e:EuclideanPlane. ∀[s1,s2,s3:Segment]. (s1 ≡ s3) supposing (s1 ≡ s2 and s2 ≡ s3)
Proof
Definitions occuring in Statement :
eu-seg-congruent: s1 ≡ s2,
eu-segment: Segment,
euclidean-plane: EuclideanPlane,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
eu-seg-congruent: s1 ≡ s2,
member: t ∈ T,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ
Lemmas referenced :
euclidean-plane_wf,
eu-segment_wf,
eu-seg-congruent_wf,
eu-congruent-transitivity,
eu-seg2_wf,
eu-seg1_wf,
sq_stable__eu-congruent
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
sqequalHypSubstitution,
cut,
lemma_by_obid,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
isectElimination,
hypothesis,
independent_functionElimination,
introduction,
because_Cache,
independent_isectElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[s1,s2,s3:Segment]. (s1 \mequiv{} s3) supposing (s1 \mequiv{} s2 and s2 \mequiv{} s3)
Date html generated:
2016_05_18-AM-06_36_46
Last ObjectModification:
2016_01_16-PM-10_30_43
Theory : euclidean!geometry
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