Nuprl Lemma : comb_for_mem_wf
λs,a,bs,z. (a ∈b bs) ∈ s:DSet ⟶ a:|s| ⟶ bs:(|s| List) ⟶ (↓True) ⟶ 𝔹
Proof
Definitions occuring in Statement :
mem: a ∈b as,
list: T List,
bool: 𝔹,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
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
Lemmas referenced :
mem_wf,
squash_wf,
true_wf,
list_wf,
set_car_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
isectElimination,
setElimination,
rename
Latex:
\mlambda{}s,a,bs,z. (a \mmember{}\msubb{} bs) \mmember{} s:DSet {}\mrightarrow{} a:|s| {}\mrightarrow{} bs:(|s| List) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbB{}
Date html generated:
2019_10_16-PM-01_02_46
Last ObjectModification:
2018_10_08-AM-11_23_29
Theory : list_2
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