Nuprl Lemma : eu-congruent-trivial
∀e:EuclideanPlane. ∀[a,b:Point]. aa=bb
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-congruent: ab=cd,
eu-point: Point,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
euclidean-plane: EuclideanPlane,
stable: Stable{P},
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
false: False,
and: P ∧ Q,
exists: ∃x:A. B[x]
Lemmas referenced :
stable__eu-congruent,
not_wf,
eu-congruent_wf,
eu-point_wf,
euclidean-plane_wf,
eu-congruent-refl,
equal_wf,
eu-extend-exists,
eu-congruence-identity,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isectElimination,
because_Cache,
independent_isectElimination,
independent_functionElimination,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
sqequalRule,
voidElimination,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
applyEquality,
lambdaEquality,
setEquality
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b:Point]. aa=bb
Date html generated:
2016_10_26-AM-07_41_03
Last ObjectModification:
2016_07_12-AM-08_07_17
Theory : euclidean!geometry
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