Nuprl Lemma : rounding-div_wf
∀[a:ℤ]. ∀[n:ℕ+]. ([a ÷ n] ∈ ℤ)
Proof
Definitions occuring in Statement :
rounding-div: [b ÷ m],
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rounding-div: [b ÷ m],
has-value: (a)↓,
uimplies: b supposing a,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
less_than: a < b,
and: P ∧ Q,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
top: Top,
bfalse: ff
Lemmas referenced :
value-type-has-value,
nat_plus_wf,
set-value-type,
less_than_wf,
int-value-type,
divrem-sq,
nat_plus_inc_int_nzero,
divide_wfa,
remainder_wfa,
lt_int_wf,
istype-top,
istype-void,
subtract_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
intEquality,
Error :lambdaEquality_alt,
natural_numberEquality,
hypothesisEquality,
Error :inhabitedIsType,
because_Cache,
applyEquality,
independent_pairEquality,
Error :lambdaFormation_alt,
productElimination,
multiplyEquality,
closedConclusion,
setElimination,
rename,
unionElimination,
equalityElimination,
lessCases,
independent_pairFormation,
baseClosed,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
axiomSqEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
promote_hyp,
voidElimination,
minusEquality,
addEquality,
Error :equalityIstype,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
Error :universeIsType
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. ([a \mdiv{} n] \mmember{} \mBbbZ{})
Date html generated:
2019_06_20-PM-01_13_28
Last ObjectModification:
2019_03_06-AM-10_51_34
Theory : int_2
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