Nuprl Lemma : q-ceil_wf
∀[r:ℚ]. (q-ceil(r) ∈ ℤ)
Proof
Definitions occuring in Statement :
q-ceil: q-ceil(r),
rationals: ℚ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
q-ceil: q-ceil(r),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
rat-int-bound_wf,
and_wf,
qless_wf,
subtract_wf,
int-subtype-rationals,
qle_wf,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
intEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[r:\mBbbQ{}]. (q-ceil(r) \mmember{} \mBbbZ{})
Date html generated:
2016_05_15-PM-11_34_56
Last ObjectModification:
2015_12_27-PM-07_27_33
Theory : rationals
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