Nuprl Lemma : comb_for_mset_for_wf

λs,g,f,a,z. (msFor{g} x ∈ a. f[x]) ∈ s:DSet ⟶ g:IAbMonoid ⟶ f:(|s| ⟶ |g|) ⟶ a:MSet{s} ⟶ (↓True) ⟶ |g|


Proof




Definitions occuring in Statement :  mset_for: mset_for,  mset: MSet{s},  so_apply: x[s],  squash: ↓T,  true: True,  member: t ∈ T,  lambda: λx.A[x],  function: x:A ⟶ B[x],  iabmonoid: IAbMonoid,  grp_car: |g|,  dset: DSet,  set_car: |p|
Definitions unfolded in proof :  member: t ∈ T,  squash: ↓T,  all: ∀x:A. B[x],  uall: ∀[x:A]. B[x],  prop: ℙ,  dset: DSet,  iabmonoid: IAbMonoid,  imon: IMonoid
Lemmas referenced :  mset_for_wf,  squash_wf,  true_wf,  mset_wf,  set_car_wf,  grp_car_wf,  iabmonoid_wf,  dset_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  lambdaEquality,  sqequalHypSubstitution,  imageElimination,  cut,  lemma_by_obid,  dependent_functionElimination,  thin,  hypothesisEquality,  equalityTransitivity,  hypothesis,  equalitySymmetry,  isectElimination,  functionEquality,  setElimination,  rename

Latex:
\mlambda{}s,g,f,a,z.  (msFor\{g\}  x  \mmember{}  a.  f[x])  \mmember{}  s:DSet  {}\mrightarrow{}  g:IAbMonoid  {}\mrightarrow{}  f:(|s|  {}\mrightarrow{}  |g|)  {}\mrightarrow{}  a:MSet\{s\}  {}\mrightarrow{}  (\mdownarrow{}True)\000C  {}\mrightarrow{}  |g|



Date html generated: 2016_05_16-AM-07_47_31
Last ObjectModification: 2015_12_28-PM-06_02_52

Theory : mset


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