Nuprl Lemma : eu-congruent-between-implies-equal
∀e:EuclideanPlane. ∀[a,b,c,x:Point]. (b = x ∈ Point) supposing (a_b_c and ab=ax and bc=xc)
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],
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,
stable: Stable{P},
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
euclidean-plane: EuclideanPlane,
false: False,
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
stable_point-eq,
eu-between-eq_wf,
eu-congruent_wf,
eu-congruence-identity-sym,
equal_wf,
eu-point_wf,
not_wf,
euclidean-plane_wf,
eu-congruent-refl,
eu-congruent-iff-length,
eu-length-flip,
eu-inner-five-segment
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
independent_functionElimination,
promote_hyp,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
setElimination,
rename,
because_Cache,
sqequalRule,
voidElimination,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
dependent_functionElimination,
productElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,x:Point]. (b = x) supposing (a\_b\_c and ab=ax and bc=xc)
Date html generated:
2016_10_26-AM-07_42_26
Last ObjectModification:
2016_07_12-AM-08_08_42
Theory : euclidean!geometry
Home
Index