Nuprl Lemma : comb_for_count_wf
λs,a,bs,z. (a #∈ bs) ∈ s:DSet ⟶ a:|s| ⟶ bs:(|s| List) ⟶ (↓True) ⟶ ℤ
Proof
Definitions occuring in Statement :
count: a #∈ as,
list: T List,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
dset: DSet
Lemmas referenced :
count_wf,
squash_wf,
true_wf,
list_wf,
set_car_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
setElimination,
rename
Latex:
\mlambda{}s,a,bs,z. (a \#\mmember{} bs) \mmember{} s:DSet {}\mrightarrow{} a:|s| {}\mrightarrow{} bs:(|s| List) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbZ{}
Date html generated:
2016_05_16-AM-07_39_30
Last ObjectModification:
2015_12_28-PM-05_43_26
Theory : list_2
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