Nuprl Lemma : eu-seg-congruent-equiv
∀e:EuclideanPlane. EquivRel(Segment;s,t.s ≡ t)
Proof
Definitions occuring in Statement :
eu-seg-congruent: s1 ≡ s2
,
eu-segment: Segment
,
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
,
prop: ℙ
,
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
eu-seg-congruent_weakening,
eu-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(Segment;s,t.s \mequiv{} t)
Date html generated:
2016_05_18-AM-06_36_52
Last ObjectModification:
2015_12_28-AM-09_25_40
Theory : euclidean!geometry
Home
Index