Nuprl Lemma : eu-cong-angle-symm2
∀e:EuclideanPlane. ∀a,b,c,x,y,z:Point. (xyz = abc ⇒ abc = xyz)
Proof
Definitions occuring in Statement :
eu-cong-angle: abc = xyz,
euclidean-plane: EuclideanPlane,
eu-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane,
eu-cong-angle: abc = xyz,
and: P ∧ Q,
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
uiff: uiff(P;Q),
uimplies: b supposing a
Lemmas referenced :
eu-congruent-iff-length,
exists_wf,
eu-congruent_wf,
eu-between-eq_wf,
euclidean-plane_wf,
eu-point_wf,
eu-cong-angle_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
productElimination,
independent_pairFormation,
dependent_pairFormation,
productEquality,
because_Cache,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_isectElimination,
equalitySymmetry
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,x,y,z:Point. (xyz = abc {}\mRightarrow{} abc = xyz)
Date html generated:
2016_06_16-PM-01_32_20
Last ObjectModification:
2016_05_23-PM-01_01_47
Theory : euclidean!geometry
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