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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