Nuprl Lemma : comb_for_mon_reduce_wf
λg,as,z. (Π as) ∈ g:IMonoid ⟶ as:(|g| List) ⟶ (↓True) ⟶ |g|
Proof
Definitions occuring in Statement :
mon_reduce: mon_reduce,
list: T List,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
imon: IMonoid,
grp_car: |g|
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
imon: IMonoid
Lemmas referenced :
mon_reduce_wf,
squash_wf,
true_wf,
list_wf,
grp_car_wf,
imon_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{}g,as,z. (\mPi{} as) \mmember{} g:IMonoid {}\mrightarrow{} as:(|g| List) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} |g|
Date html generated:
2019_10_16-PM-01_01_48
Last ObjectModification:
2018_10_08-AM-11_47_02
Theory : list_2
Home
Index