### Nuprl Lemma : single-valued-bag-single

`∀[T:Type]. ∀[b:T].  single-valued-bag({b};T)`

Proof

Definitions occuring in Statement :  single-valued-bag: `single-valued-bag(b;T)` single-bag: `{x}` uall: `∀[x:A]. B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` uimplies: `b supposing a` top: `Top` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` single-valued-bag: `single-valued-bag(b;T)`
Lemmas referenced :  single-valued-bag-if-le1 single-bag_wf bag_size_single_lemma false_wf bag-member_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin because_Cache dependent_functionElimination hypothesisEquality hypothesis independent_isectElimination sqequalRule isect_memberEquality voidElimination voidEquality independent_pairFormation lambdaFormation natural_numberEquality lambdaEquality axiomEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[b:T].    single-valued-bag(\{b\};T)

Date html generated: 2016_05_15-PM-02_42_36
Last ObjectModification: 2015_12_27-AM-09_39_43

Theory : bags

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