### Nuprl Lemma : assert-bag-null

`∀[T:Type]. ∀[bs:bag(T)].  uiff(↑bag-null(bs);bs = {} ∈ bag(T))`

Proof

Definitions occuring in Statement :  bag-null: `bag-null(bs)` empty-bag: `{}` bag: `bag(T)` assert: `↑b` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` prop: `ℙ` all: `∀x:A. B[x]` implies: `P `` Q` bag: `bag(T)` quotient: `x,y:A//B[x; y]` squash: `↓T` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` true: `True` subtype_rel: `A ⊆r B` bag-null: `bag-null(bs)` empty-bag: `{}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` assert: `↑b` ifthenelse: `if b then t else f fi ` null: `null(as)` nil: `[]` it: `⋅` btrue: `tt`
Lemmas referenced :  assert_wf bag-null_wf assert_witness equal-wf-T-base bag_wf list_wf permutation_wf permutation_weakening equal-wf-base equal_wf squash_wf true_wf quotient-member-eq permutation-equiv empty-bag_wf assert_of_null length_wf_nat nat_wf subtype_rel_set list-subtype-bag
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut independent_pairFormation hypothesis extract_by_obid sqequalHypSubstitution isectElimination thin dependent_functionElimination cumulativity hypothesisEquality equalityTransitivity equalitySymmetry independent_functionElimination baseClosed sqequalRule productElimination independent_pairEquality isect_memberEquality axiomEquality because_Cache universeEquality promote_hyp lambdaFormation independent_isectElimination pointwiseFunctionality pertypeElimination productEquality applyEquality lambdaEquality imageElimination natural_numberEquality imageMemberEquality dependent_set_memberEquality hyp_replacement applyLambdaEquality

Latex:
\mforall{}[T:Type].  \mforall{}[bs:bag(T)].    uiff(\muparrow{}bag-null(bs);bs  =  \{\})

Date html generated: 2017_10_01-AM-08_45_38
Last ObjectModification: 2017_07_26-PM-04_30_50

Theory : bags

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