Nuprl Lemma : comb_for_oal_bpos_wf
λs,g,ps,z. pos(ps) ∈ s:LOSet ⟶ g:AbDMon ⟶ ps:|oal(s;g)| ⟶ (↓True) ⟶ 𝔹
Proof
Definitions occuring in Statement :
oal_bpos: pos(ps),
oalist: oal(a;b),
bool: 𝔹,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
dset: DSet
Lemmas referenced :
oal_bpos_wf,
squash_wf,
true_wf,
set_car_wf,
oalist_wf,
dset_wf,
abdmonoid_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
isectElimination,
applyEquality,
setElimination,
rename,
sqequalRule
Latex:
\mlambda{}s,g,ps,z. pos(ps) \mmember{} s:LOSet {}\mrightarrow{} g:AbDMon {}\mrightarrow{} ps:|oal(s;g)| {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbB{}
Date html generated:
2016_05_16-AM-08_20_27
Last ObjectModification:
2015_12_28-PM-06_25_17
Theory : polynom_2
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