### Nuprl Lemma : mset_union_ident_r

`∀s:DSet. ∀a:MSet{s}.  ((a ⋃ 0{s}) = a ∈ MSet{s})`

Proof

Definitions occuring in Statement :  mset_union: `a ⋃ b` null_mset: `0{s}` mset: `MSet{s}` all: `∀x:A. B[x]` equal: `s = t ∈ T` dset: `DSet`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q` squash: `↓T` uall: `∀[x:A]. B[x]` prop: `ℙ` dset: `DSet` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` nat: `ℕ` true: `True` so_apply: `x[s]` uimplies: `b supposing a` guard: `{T}` null_mset: `0{s}` mset_count: `x #∈ a` top: `Top` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` decidable: `Dec(P)` or: `P ∨ Q` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` bfalse: `ff`
Lemmas referenced :  eq_mset_iff_eq_counts mset_union_wf null_mset_wf all_wf squash_wf true_wf set_car_wf equal_wf mset_count_union mset_count_wf nat_wf iff_weakening_equal mset_wf dset_wf count_nil_lemma imax_unfold le_int_wf bool_wf uiff_transitivity equal-wf-T-base assert_wf le_wf eqtt_to_assert assert_of_le_int decidable__equal_int nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformnot_wf intformeq_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_formula_prop_eq_lemma int_formula_prop_wf lt_int_wf less_than_wf bnot_wf eqff_to_assert assert_functionality_wrt_uiff bnot_of_le_int assert_of_lt_int
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality hypothesis productElimination independent_functionElimination applyEquality lambdaEquality imageElimination isectElimination equalityTransitivity equalitySymmetry functionEquality cumulativity universeEquality setElimination rename sqequalRule because_Cache intEquality natural_numberEquality imageMemberEquality baseClosed independent_isectElimination isect_memberEquality voidElimination voidEquality unionElimination equalityElimination applyLambdaEquality dependent_pairFormation int_eqEquality independent_pairFormation computeAll

Latex:
\mforall{}s:DSet.  \mforall{}a:MSet\{s\}.    ((a  \mcup{}  0\{s\})  =  a)

Date html generated: 2017_10_01-AM-09_59_59
Last ObjectModification: 2017_03_03-PM-01_00_59

Theory : mset

Home Index