Nuprl Lemma : member-less_than'
∀[a,b:ℤ]. Ax ∈ less_than'(a;b) supposing less_than'(a;b)
Proof
Definitions occuring in Statement :
less_than': less_than'(a;b),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
less_than': less_than'(a;b),
prop: ℙ,
top: Top,
true: True,
false: False
Lemmas referenced :
less_than'_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
intEquality,
lessCases,
axiomSqEquality,
voidElimination,
voidEquality,
natural_numberEquality
Latex:
\mforall{}[a,b:\mBbbZ{}]. Ax \mmember{} less\_than'(a;b) supposing less\_than'(a;b)
Date html generated:
2019_06_20-AM-11_19_52
Last ObjectModification:
2018_08_21-PM-10_49_28
Theory : basic_types
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