Nuprl Lemma : upper_subtype_upper
∀[m1,m2:ℤ]. {m1...} ⊆r {m2...} supposing m2 ≤ m1
Proof
Definitions occuring in Statement :
int_upper: {i...},
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
le: A ≤ B,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
int_upper_subtype_int_upper,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality
Latex:
\mforall{}[m1,m2:\mBbbZ{}]. \{m1...\} \msubseteq{}r \{m2...\} supposing m2 \mleq{} m1
Date html generated:
2018_05_21-PM-00_03_58
Last ObjectModification:
2018_05_19-AM-07_10_33
Theory : int_1
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