Nuprl Lemma : mon_for_wf
∀g:IMonoid. ∀A:Type. ∀as:A List. ∀f:A ⟶ |g|. (For{g} x ∈ as. f[x] ∈ |g|)
Proof
Definitions occuring in Statement :
mon_for: For{g} x ∈ as. f[x],
list: T List,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
imon: IMonoid,
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
mon_for: For{g} x ∈ as. f[x],
uall: ∀[x:A]. B[x],
imon: IMonoid,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
for_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
istype-universe,
list_wf,
imon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
because_Cache,
hypothesis,
lambdaEquality_alt,
applyEquality,
functionIsType,
universeIsType,
universeEquality
Latex:
\mforall{}g:IMonoid. \mforall{}A:Type. \mforall{}as:A List. \mforall{}f:A {}\mrightarrow{} |g|. (For\{g\} x \mmember{} as. f[x] \mmember{} |g|)
Date html generated:
2019_10_16-PM-01_02_18
Last ObjectModification:
2018_10_08-AM-11_49_28
Theory : list_2
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