Nuprl Lemma : eu-length_wf
∀[e:EuclideanPlane]. ∀[s:Segment]. (|s| ∈ {p:Point| O_X_p} )
Proof
Definitions occuring in Statement :
eu-length: |s|,
eu-segment: Segment,
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-X: X,
eu-O: O,
eu-point: Point,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eu-length: |s|,
all: ∀x:A. B[x],
euclidean-plane: EuclideanPlane,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
eu-extend-property,
eu-O_wf,
eu-not-colinear-OXY,
eu-X_wf,
not_wf,
equal_wf,
eu-point_wf,
eu-seg1_wf,
eu-seg2_wf,
eu-extend_wf,
eu-between-eq_wf,
eu-segment_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
setElimination,
rename,
hypothesis,
because_Cache,
productElimination,
dependent_set_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[s:Segment]. (|s| \mmember{} \{p:Point| O\_X\_p\} )
Date html generated:
2016_10_26-AM-07_41_37
Last ObjectModification:
2016_09_20-AM-10_56_33
Theory : euclidean!geometry
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