Nuprl Lemma : exp-rem_wf
∀[m:ℕ+]. ∀[i:ℤ]. ∀[n:ℕ]. (exp-rem(i;n;m) ∈ ℤ)
Proof
Definitions occuring in Statement :
exp-rem: exp-rem(i;n;m),
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
nat_plus: ℕ+,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
exp-rem: exp-rem(i;n;m),
less_than: a < b,
true: True,
nequal: a ≠ b ∈ T ,
sq_type: SQType(T),
squash: ↓T,
has-value: (a)↓
Lemmas referenced :
true_wf,
int-value-type,
equal_wf,
value-type-has-value,
div_mono1,
div_bounds_1,
int_subtype_base,
subtype_base_sq,
nat_plus_wf,
nat_wf,
int_term_value_add_lemma,
itermAdd_wf,
decidable__lt,
le_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
lelt_wf,
false_wf,
int_seg_subtype,
decidable__equal_int,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
nat_plus_properties,
int_seg_properties,
int_seg_wf,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
productElimination,
unionElimination,
applyEquality,
setEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
addEquality,
divideEquality,
addLevel,
instantiate,
cumulativity,
imageMemberEquality,
baseClosed,
remainderEquality,
callbyvalueReduce,
multiplyEquality
Latex:
\mforall{}[m:\mBbbN{}\msupplus{}]. \mforall{}[i:\mBbbZ{}]. \mforall{}[n:\mBbbN{}]. (exp-rem(i;n;m) \mmember{} \mBbbZ{})
Date html generated:
2016_05_15-PM-04_48_15
Last ObjectModification:
2016_01_16-AM-11_27_53
Theory : general
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