Nuprl Lemma : geo-add-length_wf1
∀[e:BasicGeometry]. ∀[x,y:{p:Point| O_X_p} ]. (x + y ∈ {p:Point| O_X_p} )
Proof
Definitions occuring in Statement :
geo-add-length: p + q,
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],
uimplies: b supposing a,
guard: {T},
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
basic-geometry: BasicGeometry,
geo-add-length: p + q,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
set_wf,
geo-between-exchange4,
geo-between-exchange3,
geo-between-inner-trans,
geo-between-symmetry,
geo-congruent_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
subtype_rel_sets,
geo-sep_wf,
geo-X_wf,
geo-between_wf,
geo-Op-sep,
geo-O_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productElimination,
lambdaFormation,
setEquality,
productEquality,
lambdaEquality,
independent_isectElimination,
instantiate,
applyEquality,
dependent_set_memberEquality,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
because_Cache,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
rename,
thin,
setElimination,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[x,y:\{p:Point| O\_X\_p\} ]. (x + y \mmember{} \{p:Point| O\_X\_p\} )
Date html generated:
2017_10_02-PM-04_53_17
Last ObjectModification:
2017_08_05-PM-04_10_19
Theory : euclidean!plane!geometry
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