Nuprl Lemma : eu-seg-congruent-equiv-proper
∀e:EuclideanPlane. EquivRel(ProperSegment;s,t.s ≡ t)
Proof
Definitions occuring in Statement :
eu-seg-congruent: s1 ≡ s2,
eu-proper-segment: ProperSegment,
euclidean-plane: EuclideanPlane,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
euclidean-plane: EuclideanPlane,
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
eu-proper-segment: ProperSegment,
prop: ℙ,
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
eu-seg-congruent_weakening,
eu-proper-segment_wf,
eu-seg-congruent_symmetry,
eu-seg-congruent_wf,
euclidean-plane_wf,
eu-seg-congruent_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
because_Cache,
isectElimination,
independent_isectElimination,
hypothesis,
setElimination,
rename,
hypothesisEquality
Latex:
\mforall{}e:EuclideanPlane. EquivRel(ProperSegment;s,t.s \mequiv{} t)
Date html generated:
2016_05_18-AM-06_36_55
Last ObjectModification:
2015_12_28-AM-09_25_29
Theory : euclidean!geometry
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