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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