Nuprl Lemma : comb_for_mon_for_wf
λg,A,as,f,z. For{g} x ∈ as. f[x] ∈ g:IMonoid ⟶ A:Type ⟶ as:(A List) ⟶ f:(A ⟶ |g|) ⟶ (↓True) ⟶ |g|
Proof
Definitions occuring in Statement :
mon_for: For{g} x ∈ as. f[x],
list: T List,
so_apply: x[s],
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type,
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_for_wf,
squash_wf,
true_wf,
istype-universe,
grp_car_wf,
list_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,
functionIsType,
setElimination,
rename,
universeEquality
Latex:
\mlambda{}g,A,as,f,z. For\{g\} x \mmember{} as. f[x] \mmember{} g:IMonoid {}\mrightarrow{} A:Type {}\mrightarrow{} as:(A List) {}\mrightarrow{} f:(A {}\mrightarrow{} |g|) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \000C|g|
Date html generated:
2019_10_16-PM-01_02_20
Last ObjectModification:
2018_10_08-AM-11_45_09
Theory : list_2
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