Nuprl Lemma : geo-zero-le
∀e:BasicGeometry. ∀[p:Length]. 0 ≤ p
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-zero-length: 0,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
squash: ↓T,
geo-le: p ≤ q,
uimplies: b supposing a,
guard: {T},
implies: P ⇒ Q,
so_apply: x[s],
basic-geometry: BasicGeometry,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
quotient: x,y:A//B[x; y],
prop: ℙ,
geo-length-type: Length,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
geo-zero-length: 0,
exists: ∃x:A. B[x],
cand: A c∧ B
Lemmas referenced :
geo-length-type_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-eq_wf,
equal-wf-base,
equal_wf,
geo-X_wf,
geo-O_wf,
geo-between_wf,
geo-point_wf,
set_wf,
geo-zero-length_wf,
geo-le_wf,
exists_wf,
subtype-geo-length-type,
and_wf,
geo-between-trivial,
geo-between-trivial2
Rules used in proof :
baseClosed,
imageMemberEquality,
imageElimination,
independent_isectElimination,
instantiate,
productEquality,
independent_functionElimination,
rename,
setElimination,
dependent_functionElimination,
lambdaEquality,
because_Cache,
applyEquality,
equalitySymmetry,
equalityTransitivity,
productElimination,
pertypeElimination,
sqequalRule,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
extract_by_obid,
pointwiseFunctionalityForEquality,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
setEquality,
dependent_set_memberEquality,
dependent_pairFormation,
independent_pairFormation
Latex:
\mforall{}e:BasicGeometry. \mforall{}[p:Length]. 0 \mleq{} p
Date html generated:
2017_10_02-PM-06_13_44
Last ObjectModification:
2017_08_05-PM-04_10_52
Theory : euclidean!plane!geometry
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