Nuprl Lemma : eu-between-eq-symmetry
∀e:EuclideanPlane. ∀[a,b,c:Point]. c_b_a supposing a_b_c
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-point: Point,
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,
member: t ∈ T,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
not: ¬A,
cand: A c∧ B,
false: False,
prop: ℙ,
squash: ↓T
Lemmas referenced :
euclidean-plane_wf,
eu-between-eq_wf,
eu-point_wf,
equal_wf,
not_wf,
and_wf,
eu-between_wf,
eu-between-sym,
eu-between-eq-def,
sq_stable__eu-between-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
isectElimination,
hypothesis,
independent_functionElimination,
introduction,
because_Cache,
productElimination,
independent_pairFormation,
independent_isectElimination,
voidElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c:Point]. c\_b\_a supposing a\_b\_c
Date html generated:
2016_05_18-AM-06_34_33
Last ObjectModification:
2016_01_16-PM-10_31_26
Theory : euclidean!geometry
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