Nuprl Lemma : mon_htfor_wf
∀g:IMonoid. ∀A:Type. ∀as:A List. ∀f:A ⟶ (A List) ⟶ |g|. (HTFor{g} h::t ∈ as. f[h;t] ∈ |g|)
Proof
Definitions occuring in Statement :
mon_htfor: HTFor{g} h::t ∈ as. f[h; t],
list: T List,
so_apply: x[s1;s2],
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_htfor: HTFor{g} h::t ∈ as. f[h; t],
uall: ∀[x:A]. B[x],
imon: IMonoid,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
for_hdtl_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,
inhabitedIsType,
functionIsType,
universeIsType,
universeEquality
Latex:
\mforall{}g:IMonoid. \mforall{}A:Type. \mforall{}as:A List. \mforall{}f:A {}\mrightarrow{} (A List) {}\mrightarrow{} |g|. (HTFor\{g\} h::t \mmember{} as. f[h;t] \mmember{} |g|)
Date html generated:
2019_10_16-PM-01_02_41
Last ObjectModification:
2018_10_08-AM-11_50_57
Theory : list_2
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