Nuprl Lemma : eu-construction-unicity
∀e:EuclideanPlane. ∀[Q,A,X,Y:Point]. (X = Y ∈ Point) supposing (AY=AX and Q_A_X and Q_A_Y and (¬(Q = A ∈ Point)))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-congruent: ab=cd,
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],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
euclidean-plane: EuclideanPlane
Lemmas referenced :
eu-congruent_wf,
eu-between-eq_wf,
not_wf,
equal_wf,
eu-point_wf,
euclidean-plane_wf,
eu-congruent-refl,
eu-five-segment,
eu-congruence-identity,
eu-congruent-symmetry,
eu-three-segment
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_isectElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[Q,A,X,Y:Point]. (X = Y) supposing (AY=AX and Q\_A\_X and Q\_A\_Y and (\mneg{}(Q = A)))
Date html generated:
2016_05_18-AM-06_35_23
Last ObjectModification:
2015_12_28-AM-09_26_46
Theory : euclidean!geometry
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