Nuprl Lemma : upper_subtype_nat
∀[m:ℤ]. {m...} ⊆r ℕ supposing 0 ≤ m
Proof
Definitions occuring in Statement : 
int_upper: {i...}
, 
nat: ℕ
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
le: A ≤ B
, 
natural_number: $n
, 
int: ℤ
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
nat: ℕ
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
int_upper_subtype_nat, 
le_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
dependent_set_memberEquality, 
hypothesisEquality, 
hypothesis, 
natural_numberEquality, 
sqequalRule, 
axiomEquality, 
isect_memberEquality, 
because_Cache, 
equalityTransitivity, 
equalitySymmetry, 
intEquality
Latex:
\mforall{}[m:\mBbbZ{}].  \{m...\}  \msubseteq{}r  \mBbbN{}  supposing  0  \mleq{}  m
Date html generated:
2018_05_21-PM-00_03_59
Last ObjectModification:
2018_05_19-AM-07_10_37
Theory : int_1
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