Nuprl Lemma : eu-seg-congruent_symmetry
∀e:EuclideanPlane. ∀[s1,s2:Segment]. s2 ≡ s1 supposing s1 ≡ s2
Proof
Definitions occuring in Statement :
eu-seg-congruent: s1 ≡ s2,
eu-segment: Segment,
euclidean-plane: EuclideanPlane,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
eu-seg-congruent: s1 ≡ s2,
member: t ∈ T,
euclidean-plane: EuclideanPlane,
prop: ℙ
Lemmas referenced :
eu-congruent-symmetry,
eu-seg1_wf,
eu-seg2_wf,
eu-seg-congruent_wf,
eu-segment_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
sqequalHypSubstitution,
cut,
lemma_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
setElimination,
rename,
hypothesis,
independent_isectElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[s1,s2:Segment]. s2 \mequiv{} s1 supposing s1 \mequiv{} s2
Date html generated:
2016_05_18-AM-06_36_48
Last ObjectModification:
2015_12_28-AM-09_25_31
Theory : euclidean!geometry
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