Nuprl Lemma : q-floor_wf
∀[r:ℚ]. ([r] ∈ ℤ)
Proof
Definitions occuring in Statement :
q-floor: [r],
rationals: ℚ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
q-floor: [r],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top
Lemmas referenced :
pi1_wf_top,
rat-int-part_wf2,
subtype_rel_set,
rationals_wf,
and_wf,
qle_wf,
int-subtype-rationals,
qless_wf,
top_wf,
equal_wf,
qadd_wf,
subtype_rel_product
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
applyEquality,
productEquality,
setEquality,
natural_numberEquality,
because_Cache,
lambdaEquality,
spreadEquality,
setElimination,
rename,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[r:\mBbbQ{}]. ([r] \mmember{} \mBbbZ{})
Date html generated:
2016_05_15-PM-11_34_40
Last ObjectModification:
2015_12_27-PM-07_27_46
Theory : rationals
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