Nuprl Lemma : eu-seg-extend_wf
∀[e:EuclideanPlane]. ∀[s:ProperSegment]. ∀[t:Segment]. (s + t ∈ ProperSegment)
Proof
Definitions occuring in Statement :
eu-seg-extend: s + t,
eu-proper-segment: ProperSegment,
eu-segment: Segment,
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eu-seg-extend: s + t,
eu-proper-segment: ProperSegment,
euclidean-plane: EuclideanPlane,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
eu-seg-proper: proper(s),
eu-segment: Segment,
eu-seg2: s.2,
eu-seg1: s.1,
pi1: fst(t),
pi2: snd(t),
false: False,
euclidean-axioms: euclidean-axioms(e),
and: P ∧ Q,
uimplies: b supposing a
Lemmas referenced :
eu-seg1_wf,
eu-extend_wf,
equal_wf,
eu-point_wf,
eu-seg2_wf,
not_wf,
eu-seg-proper_wf,
eu-segment_wf,
eu-proper-segment_wf,
euclidean-plane_wf,
eu-between-eq_wf,
eu-congruent_wf,
eu-between-eq-same
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
independent_pairEquality,
extract_by_obid,
isectElimination,
because_Cache,
hypothesis,
hypothesisEquality,
lambdaFormation,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
independent_functionElimination,
productElimination,
hyp_replacement,
Error :applyLambdaEquality,
productEquality,
independent_isectElimination,
voidElimination
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[s:ProperSegment]. \mforall{}[t:Segment]. (s + t \mmember{} ProperSegment)
Date html generated:
2016_10_26-AM-07_41_34
Last ObjectModification:
2016_07_12-AM-08_07_44
Theory : euclidean!geometry
Home
Index