### Nuprl Lemma : fset_properties

`∀s:DSet. ∀a:FiniteSet{s}.  {∀x:|s|. ((x #∈ a) ≤ 1)}`

Proof

Definitions occuring in Statement :  finite_set: `FiniteSet{s}` mset_count: `x #∈ a` guard: `{T}` le: `A ≤ B` all: `∀x:A. B[x]` natural_number: `\$n` dset: `DSet` set_car: `|p|`
Definitions unfolded in proof :  guard: `{T}` all: `∀x:A. B[x]` finite_set: `FiniteSet{s}` member: `t ∈ T` uall: `∀[x:A]. B[x]` dset: `DSet` subtype_rel: `A ⊆r B` nat: `ℕ` sq_stable: `SqStable(P)` implies: `P `` Q` squash: `↓T`
Lemmas referenced :  nat_wf mset_count_wf sq_stable__le dset_wf finite_set_wf set_car_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation sqequalHypSubstitution setElimination thin rename cut lemma_by_obid isectElimination hypothesisEquality hypothesis dependent_functionElimination applyEquality lambdaEquality natural_numberEquality independent_functionElimination introduction imageMemberEquality baseClosed imageElimination

Latex:
\mforall{}s:DSet.  \mforall{}a:FiniteSet\{s\}.    \{\mforall{}x:|s|.  ((x  \#\mmember{}  a)  \mleq{}  1)\}

Date html generated: 2016_05_16-AM-07_50_56
Last ObjectModification: 2016_01_16-PM-11_39_14

Theory : mset

Home Index