Nuprl Lemma : geo-congruent-comm
∀e:EuclideanPlane. ∀[a,b,c,d:Point]. ba ≅ dc supposing ab ≅ cd
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-congruent_wf,
geo-congruent-right-comm,
geo-congruent-left-comm
Rules used in proof :
sqequalRule,
instantiate,
applyEquality,
because_Cache,
hypothesis,
independent_isectElimination,
isectElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,d:Point]. ba \00D0 dc supposing ab \00D0 cd
Date html generated:
2017_10_02-PM-03_28_49
Last ObjectModification:
2017_08_04-PM-09_29_50
Theory : euclidean!plane!geometry
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