Nuprl Lemma : eu-between-eq-same-side2
∀e:EuclideanPlane. ∀[A,B,C,D:Point]. (¬((¬B_C_D) ∧ (¬B_D_C))) supposing ((¬(A = B ∈ Point)) and A_B_C and A_B_D)
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,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
false: False,
prop: ℙ,
euclidean-plane: EuclideanPlane
Lemmas referenced :
eu-between-eq-same-side,
eu-between-eq-symmetry,
eu-between-eq-inner-trans,
eu-between-eq-exchange3,
eu-between-eq_wf,
and_wf,
not_wf,
equal_wf,
eu-point_wf,
euclidean-plane_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberFormation,
isectElimination,
introduction,
independent_isectElimination,
independent_functionElimination,
independent_pairFormation,
productElimination,
promote_hyp,
because_Cache,
voidElimination,
setElimination,
rename,
sqequalRule,
lambdaEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[A,B,C,D:Point]. (\mneg{}((\mneg{}B\_C\_D) \mwedge{} (\mneg{}B\_D\_C))) supposing ((\mneg{}(A = B)) and A\_B\_C and A\_B\_D)
Date html generated:
2016_05_18-AM-06_39_50
Last ObjectModification:
2015_12_28-AM-09_23_35
Theory : euclidean!geometry
Home
Index