Nuprl Lemma : geo-le_functionality_wrt_implies
∀[e:BasicGeometry]. ∀[a,b,c,d:Length]. ({a ≤ d supposing b ≤ c}) supposing (c ≤ d and geo_ge(e; b; a))
Proof
Definitions occuring in Statement :
geo_ge: geo_ge(e; p; q),
geo-le: p ≤ q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T}
Definitions unfolded in proof :
prop: ℙ,
squash: ↓T,
geo-le: p ≤ q,
guard: {T},
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
geo_ge: geo_ge(e; p; q),
all: ∀x:A. B[x]
Lemmas referenced :
basic-geometry_wf,
geo-length-type_wf,
geo_ge_wf,
geo-le_wf,
geo-le_transitivity
Rules used in proof :
because_Cache,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
isectElimination,
extract_by_obid,
baseClosed,
thin,
hypothesisEquality,
imageMemberEquality,
hypothesis,
imageElimination,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_isectElimination,
dependent_functionElimination
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a,b,c,d:Length].
(\{a \mleq{} d supposing b \mleq{} c\}) supposing (c \mleq{} d and geo\_ge(e; b; a))
Date html generated:
2017_10_02-PM-04_52_35
Last ObjectModification:
2017_08_05-AM-09_10_14
Theory : euclidean!plane!geometry
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