Nuprl Lemma : comb_for_oal_inj_wf
λa,b,k,v,z. inj(k,v) ∈ a:LOSet ⟶ b:AbDMon ⟶ k:|a| ⟶ v:|b| ⟶ (↓True) ⟶ |oal(a;b)|
Proof
Definitions occuring in Statement :
oal_inj: inj(k,v),
oalist: oal(a;b),
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
abdmonoid: AbDMon,
grp_car: |g|,
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,
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet
Lemmas referenced :
oal_inj_wf,
squash_wf,
true_wf,
grp_car_wf,
set_car_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,
setElimination,
rename
Latex:
\mlambda{}a,b,k,v,z. inj(k,v) \mmember{} a:LOSet {}\mrightarrow{} b:AbDMon {}\mrightarrow{} k:|a| {}\mrightarrow{} v:|b| {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} |oal(a;b)|
Date html generated:
2016_05_16-AM-08_18_43
Last ObjectModification:
2015_12_28-PM-06_26_32
Theory : polynom_2
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