Nuprl Lemma : comb_for_rng_mssum_wf
λs,r,f,a,z. Σx ∈ a. f[x] ∈ s:DSet ⟶ r:Rng ⟶ f:(|s| ⟶ |r|) ⟶ a:MSet{s} ⟶ (↓True) ⟶ |r|
Proof
Definitions occuring in Statement : 
rng_mssum: rng_mssum, 
mset: MSet{s}
, 
so_apply: x[s]
, 
squash: ↓T
, 
true: True
, 
member: t ∈ T
, 
lambda: λx.A[x]
, 
function: x:A ⟶ B[x]
, 
rng: Rng
, 
rng_car: |r|
, 
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
, 
rng: Rng
Lemmas referenced : 
rng_mssum_wf, 
squash_wf, 
true_wf, 
mset_wf, 
set_car_wf, 
rng_car_wf, 
rng_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,r,f,a,z.  \mSigma{}x  \mmember{}  a.  f[x]  \mmember{}  s:DSet  {}\mrightarrow{}  r:Rng  {}\mrightarrow{}  f:(|s|  {}\mrightarrow{}  |r|)  {}\mrightarrow{}  a:MSet\{s\}  {}\mrightarrow{}  (\mdownarrow{}True)  {}\mrightarrow{}  |r|
Date html generated:
2016_05_16-AM-08_11_50
Last ObjectModification:
2015_12_28-PM-06_06_13
Theory : list_3
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