### Nuprl Lemma : bdd-diff-equiv

`EquivRel(ℕ+ ⟶ ℤ;f,g.bdd-diff(f;g))`

Proof

Definitions occuring in Statement :  bdd-diff: `bdd-diff(f;g)` equiv_rel: `EquivRel(T;x,y.E[x; y])` nat_plus: `ℕ+` function: `x:A ⟶ B[x]` int: `ℤ`
Definitions unfolded in proof :  equiv_rel: `EquivRel(T;x,y.E[x; y])` and: `P ∧ Q` refl: `Refl(T;x,y.E[x; y])` all: `∀x:A. B[x]` member: `t ∈ T` cand: `A c∧ B` sym: `Sym(T;x,y.E[x; y])` implies: `P `` Q` prop: `ℙ` uall: `∀[x:A]. B[x]` trans: `Trans(T;x,y.E[x; y])` bdd-diff: `bdd-diff(f;g)` exists: `∃x:A. B[x]` nat: `ℕ` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` squash: `↓T` nat_plus: `ℕ+` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` true: `True` subtype_rel: `A ⊆r B` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtract: `n - m` ge: `i ≥ j ` uiff: `uiff(P;Q)` rev_uimplies: `rev_uimplies(P;Q)`
Lemmas referenced :  nat_plus_wf bdd-diff_wf false_wf le_wf squash_wf true_wf absval_pos subtract_wf nat_plus_properties decidable__le less_than_wf satisfiable-full-omega-tt intformnot_wf intformle_wf itermConstant_wf itermSubtract_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_subtract_lemma int_term_value_var_lemma int_formula_prop_wf iff_weakening_equal all_wf absval_wf absval_sym minus-add minus-minus minus-one-mul add-commutes nat_wf nat_properties intformand_wf itermAdd_wf int_formula_prop_and_lemma int_term_value_add_lemma decidable__equal_int intformeq_wf itermMinus_wf int_formula_prop_eq_lemma int_term_value_minus_lemma add-is-int-iff subtract-is-int-iff and_wf equal_wf le_functionality le_weakening int-triangle-inequality add_functionality_wrt_le
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity independent_pairFormation lambdaFormation functionEquality cut introduction extract_by_obid hypothesis intEquality sqequalHypSubstitution isectElimination thin functionExtensionality applyEquality hypothesisEquality because_Cache dependent_pairFormation dependent_set_memberEquality natural_numberEquality sqequalRule lambdaEquality imageElimination equalityTransitivity equalitySymmetry setElimination rename dependent_functionElimination unionElimination independent_isectElimination int_eqEquality isect_memberEquality voidElimination voidEquality computeAll imageMemberEquality baseClosed universeEquality productElimination independent_functionElimination multiplyEquality minusEquality addEquality pointwiseFunctionality promote_hyp baseApply closedConclusion setEquality hyp_replacement Error :applyLambdaEquality

Latex:
EquivRel(\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{};f,g.bdd-diff(f;g))

Date html generated: 2016_10_26-AM-09_02_38
Last ObjectModification: 2016_07_12-AM-08_12_54

Theory : reals

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