Nuprl Lemma : geo-congruence-identity-sym
∀[e:EuclideanPlane]. ∀[a,b,c:Point]. a ≡ b supposing ab ≅ cc
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-eq: a ≡ b,
geo-congruent: ab ≅ cd,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
geo-eq: a ≡ b,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
geo-congruent_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-sep_wf,
geo-congruent-symmetry,
geo-congruence-identity
Rules used in proof :
voidElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
isectElimination,
extract_by_obid,
because_Cache,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[a,b,c:Point]. a \mequiv{} b supposing ab \00D0 cc
Date html generated:
2017_10_02-PM-03_28_01
Last ObjectModification:
2017_08_08-PM-00_35_23
Theory : euclidean!plane!geometry
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