Nuprl Lemma : q-rel_wf
∀[r:ℤ]. ∀[x:ℚ]. (q-rel(r;x) ∈ ℙ)
Proof
Definitions occuring in Statement :
q-rel: q-rel(r;x),
rationals: ℚ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
q-rel: q-rel(r;x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
ifthenelse_wf,
eq_int_wf,
equal_wf,
rationals_wf,
int-subtype-rationals,
qle_wf,
qless_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
natural_numberEquality,
hypothesis,
universeEquality,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
intEquality
Latex:
\mforall{}[r:\mBbbZ{}]. \mforall{}[x:\mBbbQ{}]. (q-rel(r;x) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-11_17_44
Last ObjectModification:
2015_12_27-PM-07_35_12
Theory : rationals
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