Nuprl Lemma : respects-equality-oalist2

∀[s:LOSet]. ∀[g:AbDMon].  respects-equality((|s| × |g|) List;|oal(s;g)|)


Proof




Definitions occuring in Statement :  oalist: oal(a;b),  list: T List,  respects-equality: respects-equality(S;T),  uall: ∀[x:A]. B[x],  product: x:A × B[x],  abdmonoid: AbDMon,  grp_car: |g|,  loset: LOSet,  set_car: |p|
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  set_car: |p|,  pi1: fst(t),  set_prod: s × t,  mk_dset: mk_dset(T, eq),  grp_car: |g|,  dset_of_mon: g↓set
Lemmas referenced :  respects-equality-oalist1,  abdmonoid_wf,  loset_wf
Rules used in proof :  cut,  introduction,  extract_by_obid,  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation_alt,  hypothesis,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesisEquality,  sqequalRule,  universeIsType

Latex:
\mforall{}[s:LOSet].  \mforall{}[g:AbDMon].    respects-equality((|s|  \mtimes{}  |g|)  List;|oal(s;g)|)



Date html generated: 2019_10_16-PM-01_07_04
Last ObjectModification: 2018_11_27-AM-11_23_17

Theory : polynom_2


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