### 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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