### Nuprl Lemma : mset_diff_wf_f

`∀s:DSet. ∀a,b:FiniteSet{s}.  (a - b ∈ FiniteSet{s})`

Proof

Definitions occuring in Statement :  mset_diff: `a - b` finite_set: `FiniteSet{s}` all: `∀x:A. B[x]` member: `t ∈ T` dset: `DSet`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]` guard: `{T}` finite_set: `FiniteSet{s}` dset: `DSet` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` nat: `ℕ` so_apply: `x[s]` prop: `ℙ` squash: `↓T` true: `True` uimplies: `b supposing a` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q` ndiff: `a -- b` le: `A ≤ B` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` less_than': `less_than'(a;b)` false: `False` not: `¬A` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` decidable: `Dec(P)` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top`
Lemmas referenced :  finite_set_wf dset_wf fset_properties mset_diff_wf set_car_wf all_wf le_wf mset_count_wf nat_wf squash_wf true_wf mset_count_diff iff_weakening_equal imax_unfold subtract_wf le_int_wf bool_wf eqtt_to_assert assert_of_le_int false_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot decidable__le nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformnot_wf itermSubtract_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_not_lemma int_term_value_subtract_lemma int_formula_prop_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut sqequalHypSubstitution hypothesis introduction extract_by_obid isectElimination thin hypothesisEquality dependent_functionElimination setElimination rename dependent_set_memberEquality because_Cache sqequalRule lambdaEquality applyEquality natural_numberEquality imageElimination equalityTransitivity equalitySymmetry intEquality imageMemberEquality baseClosed universeEquality independent_isectElimination productElimination independent_functionElimination unionElimination equalityElimination independent_pairFormation dependent_pairFormation promote_hyp instantiate cumulativity voidElimination applyLambdaEquality int_eqEquality isect_memberEquality voidEquality computeAll

Latex:
\mforall{}s:DSet.  \mforall{}a,b:FiniteSet\{s\}.    (a  -  b  \mmember{}  FiniteSet\{s\})

Date html generated: 2017_10_01-AM-10_00_28
Last ObjectModification: 2017_03_03-PM-01_01_47

Theory : mset

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