Nuprl Lemma : geo-le_weakening-lt
∀[e:BasicGeometry]. ∀[p,q:Length]. p ≤ q supposing p < q
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-le: p ≤ q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
guard: {T},
geo_ge: geo_ge(e; p; q),
rev_uimplies: rev_uimplies(P;Q),
all: ∀x:A. B[x],
basic-geometry: BasicGeometry,
prop: ℙ,
squash: ↓T,
geo-le: p ≤ q,
and: P ∧ Q,
exists: ∃x:A. B[x],
geo-lt: p < q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-le_weakening,
geo-le_functionality_wrt_implies,
geo-le-add1,
geo-mk-seg_wf,
geo-length_wf,
geo-add-length_wf,
basic-geometry_wf,
geo-length-type_wf,
geo-lt_wf
Rules used in proof :
independent_isectElimination,
dependent_functionElimination,
rename,
setElimination,
equalitySymmetry,
equalityTransitivity,
because_Cache,
isect_memberEquality,
isectElimination,
extract_by_obid,
baseClosed,
hypothesisEquality,
imageMemberEquality,
hypothesis,
imageElimination,
sqequalRule,
thin,
productElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[p,q:Length]. p \mleq{} q supposing p < q
Date html generated:
2017_10_02-PM-06_18_48
Last ObjectModification:
2017_08_05-PM-04_13_24
Theory : euclidean!plane!geometry
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