Nuprl Lemma : set-add_wf

∀[a,b:coSet{i:l}].  (a + b ∈ coSet{i:l})


Proof




Definitions occuring in Statement :  set-add: a + b,  coSet: coSet{i:l},  uall: ∀[x:A]. B[x],  member: t ∈ T
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  subtype_rel: A ⊆r B,  set-add: a + b,  mk-coset: mk-coset(T;f),  all: ∀x:A. B[x],  implies: P ⇒ Q,  prop: ℙ
Lemmas referenced :  subtype_coSet,  coSet_subtype,  mk-coset_wf,  equal_wf,  coSet_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation,  introduction,  cut,  hypothesis_subsumption,  extract_by_obid,  hypothesis,  hypothesisEquality,  applyEquality,  sqequalHypSubstitution,  sqequalRule,  productElimination,  thin,  isectElimination,  unionEquality,  lambdaEquality,  equalityTransitivity,  equalitySymmetry,  lambdaFormation,  unionElimination,  dependent_functionElimination,  independent_functionElimination,  axiomEquality,  isect_memberEquality,  because_Cache

Latex:
\mforall{}[a,b:coSet\{i:l\}].    (a  +  b  \mmember{}  coSet\{i:l\})



Date html generated: 2019_10_31-AM-06_33_20
Last ObjectModification: 2018_08_21-PM-02_01_17

Theory : constructive!set!theory


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