Nuprl Lemma : geo-length_wf1
∀[e:BasicGeometry]. ∀[s:geo-segment(e)]. (|s| ∈ {p:Point| O_X_p} )
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-segment: geo-segment(e),
basic-geometry: BasicGeometry,
geo-X: X,
geo-O: O,
geo-between: a_b_c,
geo-point: Point,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
cand: A c∧ B,
implies: P ⇒ Q,
so_apply: x[s],
and: P ∧ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
basic-geometry: BasicGeometry,
geo-length: |s|,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-segment_wf,
geo-point_wf,
geo-congruent_wf,
geo-between_wf,
subtype_rel_sets,
geo-seg2_wf,
geo-seg1_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-sep_wf,
geo-X_wf,
geo-sep-O-X,
geo-O_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productElimination,
lambdaFormation,
setEquality,
productEquality,
lambdaEquality,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
dependent_set_memberEquality,
dependent_functionElimination,
hypothesis,
because_Cache,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[s:geo-segment(e)]. (|s| \mmember{} \{p:Point| O\_X\_p\} )
Date html generated:
2017_10_02-PM-04_51_45
Last ObjectModification:
2017_08_05-AM-09_09_56
Theory : euclidean!plane!geometry
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