Nuprl Lemma : int_seg_inc
∀[i,j:ℤ]. ({i..j-} ⊆r ℚ)
Proof
Definitions occuring in Statement :
rationals: ℚ,
int_seg: {i..j-},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_set,
rationals_wf,
lelt_wf,
int-subtype-rationals
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesis,
lambdaEquality,
hypothesisEquality,
independent_isectElimination,
axiomEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[i,j:\mBbbZ{}]. (\{i..j\msupminus{}\} \msubseteq{}r \mBbbQ{})
Date html generated:
2019_10_16-AM-11_47_02
Last ObjectModification:
2018_09_17-PM-06_26_52
Theory : rationals
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