Nuprl Lemma : comb_for_mod_mssum_wf
λs,r,m,f,a,z. Σm x ∈ a. f[x] ∈ s:DSet ⟶ r:Rng ⟶ m:r-Module ⟶ f:(|s| ⟶ m.car) ⟶ a:MSet{s} ⟶ (↓True) ⟶ m.car
Proof
Definitions occuring in Statement :
mod_mssum: mod_mssum,
mset: MSet{s},
module: A-Module,
alg_car: a.car,
so_apply: x[s],
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
rng: Rng,
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,
module: A-Module
Lemmas referenced :
mod_mssum_wf,
squash_wf,
true_wf,
mset_wf,
set_car_wf,
alg_car_wf,
rng_car_wf,
module_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,m,f,a,z. \mSigma{}m x \mmember{} a. f[x] \mmember{} s:DSet
{}\mrightarrow{} r:Rng
{}\mrightarrow{} m:r-Module
{}\mrightarrow{} f:(|s| {}\mrightarrow{} m.car)
{}\mrightarrow{} a:MSet\{s\}
{}\mrightarrow{} (\mdownarrow{}True)
{}\mrightarrow{} m.car
Date html generated:
2016_05_16-AM-08_12_07
Last ObjectModification:
2015_12_28-PM-06_06_13
Theory : list_3
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