Nuprl Lemma : geo-lt_functionality_wrt_implies
∀e:BasicGeometry. ∀a,b,c,d:Length. (geo_ge(e; b; a) ⇒ c ≤ d ⇒ {b < c ⇒ a < d})
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo_ge: geo_ge(e; p; q),
geo-le: p ≤ q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
guard: {T},
implies: P ⇒ Q,
all: ∀x:A. B[x],
geo_ge: geo_ge(e; p; q),
squash: ↓T,
geo-le: p ≤ q
Lemmas referenced :
basic-geometry_wf,
geo-length-type_wf,
geo_ge_wf,
geo-le_wf,
geo-lt_wf,
geo-lt_transitivity2,
geo-lt_transitivity
Rules used in proof :
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
because_Cache,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,d:Length. (geo\_ge(e; b; a) {}\mRightarrow{} c \mleq{} d {}\mRightarrow{} \{b < c {}\mRightarrow{} a < d\})
Date html generated:
2017_10_02-PM-06_19_07
Last ObjectModification:
2017_08_05-PM-04_13_41
Theory : euclidean!plane!geometry
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