Nuprl Lemma : geo-length-equality
∀e:BasicGeometry. ∀p':{p:Point| O_X_p} . (|Xp'| = p' ∈ Length)
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-X: X,
geo-O: O,
geo-between: a_b_c,
geo-point: Point,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
guard: {T},
top: Top,
geo-length: |s|,
implies: P ⇒ Q,
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
basic-geometry: BasicGeometry,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
geo-length-type: Length,
all: ∀x:A. B[x],
and: P ∧ Q,
squash: ↓T,
sq_stable: SqStable(P)
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
set_wf,
geo_seg2_mk_seg_lemma,
geo_seg1_mk_seg_lemma,
geo-mk-seg_wf,
geo-length_wf1,
geo-length-equiv,
geo-eq_wf,
geo-X_wf,
geo-O_wf,
geo-between_wf,
geo-point_wf,
quotient-member-eq,
equal_wf,
geo-congruent_wf,
geo-sep_wf,
geo-sep-O-X,
geo-eq_inversion,
sq_stable__geo-between,
geo-between-symmetry,
geo-construction-unicity
Rules used in proof :
instantiate,
voidEquality,
voidElimination,
isect_memberEquality,
independent_functionElimination,
independent_isectElimination,
lambdaEquality,
rename,
setElimination,
dependent_functionElimination,
hypothesis,
because_Cache,
applyEquality,
hypothesisEquality,
setEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
equalitySymmetry,
equalityTransitivity,
productEquality,
dependent_set_memberEquality,
imageElimination,
baseClosed,
imageMemberEquality,
productElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}p':\{p:Point| O\_X\_p\} . (|Xp'| = p')
Date html generated:
2017_10_02-PM-04_52_49
Last ObjectModification:
2017_08_05-AM-09_10_29
Theory : euclidean!plane!geometry
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