Nuprl Lemma : eu-congruence-identity-sym
∀[e:EuclideanPlane]. ∀[a,b,c:Point]. a = b ∈ Point supposing cc=ab
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-congruent: ab=cd,
eu-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
euclidean-plane: EuclideanPlane,
all: ∀x:A. B[x]
Lemmas referenced :
eu-congruent_wf,
eu-point_wf,
euclidean-plane_wf,
eu-congruent-symmetry,
eu-congruence-identity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
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{}[a,b,c:Point]. a = b supposing cc=ab
Date html generated:
2016_05_18-AM-06_35_09
Last ObjectModification:
2015_12_28-AM-09_26_14
Theory : euclidean!geometry
Home
Index