Nuprl Lemma : not-lt-and-eq
∀[e:BasicGeometry]. ∀[p,q:Length]. ((p = q ∈ Length) ⇒ q < p ⇒ False)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
false: False,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
false: False,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q
Lemmas referenced :
geo-lt_wf,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal,
geo-lt-irrefl,
geo-length-type_wf,
basic-geometry_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
applyEquality,
thin,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
voidElimination,
equalityIstype,
inhabitedIsType,
dependent_functionElimination,
functionIsTypeImplies,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[p,q:Length]. ((p = q) {}\mRightarrow{} q < p {}\mRightarrow{} False)
Date html generated:
2019_10_16-PM-01_19_31
Last ObjectModification:
2019_01_31-PM-09_32_41
Theory : euclidean!plane!geometry
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