Nuprl Lemma : int_seg_subtype-nat
∀[m,n:ℤ]. {m..n-} ⊆r ℕ supposing 0 ≤ m
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
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,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
int_seg_subtype_nat,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
axiomEquality,
natural_numberEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality
Latex:
\mforall{}[m,n:\mBbbZ{}]. \{m..n\msupminus{}\} \msubseteq{}r \mBbbN{} supposing 0 \mleq{} m
Date html generated:
2016_05_13-PM-04_02_01
Last ObjectModification:
2015_12_26-AM-10_56_47
Theory : int_1
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