### Nuprl Lemma : bag-subtract-no-repeats

`∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs,as:bag(T)].  bag-no-repeats(T;bag-subtract(eq;bs;as)) supposing bag-no-repeats(T;bs)`

Proof

Definitions occuring in Statement :  bag-subtract: `bag-subtract(eq;bs;as)` bag-no-repeats: `bag-no-repeats(T;bs)` bag: `bag(T)` deq: `EqDecider(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` bag-no-repeats: `bag-no-repeats(T;bs)` squash: `↓T` prop: `ℙ` all: `∀x:A. B[x]` implies: `P `` Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_stable: `SqStable(P)` exists: `∃x:A. B[x]` subtype_rel: `A ⊆r B` bag-subtract: `bag-subtract(eq;bs;as)` bag-accum: `bag-accum(v,x.f[v; x];init;bs)` top: `Top` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` or: `P ∨ Q` and: `P ∧ Q` true: `True` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` uiff: `uiff(P;Q)`
Lemmas referenced :  bag-no-repeats_wf bag_wf deq_wf bag-subtract_wf squash_wf all_wf bag_to_squash_list sq_stable__all sq_stable__bag-no-repeats list_induction list-subtype-bag list_wf list_accum_nil_lemma list_accum_cons_lemma bag-drop_wf bag-drop-property true_wf iff_weakening_equal bag-no-repeats-append single-bag_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution imageElimination hypothesis imageMemberEquality hypothesisEquality thin baseClosed extract_by_obid isectElimination cumulativity isect_memberEquality because_Cache equalityTransitivity equalitySymmetry universeEquality dependent_functionElimination independent_functionElimination lambdaEquality functionEquality lambdaFormation productElimination promote_hyp rename applyEquality independent_isectElimination hyp_replacement Error :applyLambdaEquality,  voidElimination voidEquality unionElimination natural_numberEquality

Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[bs,as:bag(T)].
bag-no-repeats(T;bag-subtract(eq;bs;as))  supposing  bag-no-repeats(T;bs)

Date html generated: 2016_10_25-AM-11_28_25
Last ObjectModification: 2016_07_12-AM-07_34_44

Theory : bags_2

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