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: supposing a top: Top le: A ≤ B and: P ∧ Q less_than': less_than'(a;b) false: False not: ¬A implies:  Q prop: 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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