Nuprl Lemma : eu-between-eq-outer-trans
∀e:EuclideanPlane. ∀[a,b,c,d:Point]. (a_c_d) supposing (b_c_d and a_b_c and (¬(b = c ∈ Point)))
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],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
squash: ↓T
Lemmas referenced :
eu-point_wf,
sq_stable__eu-between-eq,
eu-between-eq_wf,
eu-between-eq-same,
equal_wf,
eu-extend-exists,
not_wf,
euclidean-plane_wf,
eu-construction-unicity,
eu-between-eq-symmetry,
eu-between-eq-inner-trans,
eu-between-eq-exchange3,
eu-congruent-symmetry
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
equalityEquality,
extract_by_obid,
isectElimination,
setElimination,
rename,
hypothesis,
because_Cache,
independent_functionElimination,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
independent_isectElimination,
dependent_set_memberEquality,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,d:Point]. (a\_c\_d) supposing (b\_c\_d and a\_b\_c and (\mneg{}(b = c)))
Date html generated:
2016_10_26-AM-07_41_13
Last ObjectModification:
2016_07_12-AM-08_07_23
Theory : euclidean!geometry
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