Nuprl Lemma : forget-group_wf
ForgetGroup ∈ Functor(Group;TypeCat)
Proof
Definitions occuring in Statement :
forget-group: ForgetGroup,
group-cat: Group,
type-cat: TypeCat,
cat-functor: Functor(C1;C2),
member: t ∈ T
Definitions unfolded in proof :
forget-group: ForgetGroup,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
cat-ob: cat-ob(C),
pi1: fst(t),
group-cat: Group,
mk-cat: mk-cat,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
type-cat: TypeCat,
monoid_hom: MonHom(M1,M2),
grp: Group{i},
mon: Mon,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
group-cat_wf,
type-cat_wf,
grp_car_wf,
mon_subtype_grp_sig,
grp_subtype_mon,
subtype_rel_transitivity,
grp_wf,
mon_wf,
grp_sig_wf,
cat-ob_wf,
cat_arrow_triple_lemma,
cat_ob_pair_lemma,
cat-arrow_wf,
cat_comp_tuple_lemma,
compose_wf,
monoid_hom_wf,
cat_id_tuple_lemma,
mk-functor_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
instantiate,
independent_isectElimination,
because_Cache,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
setElimination,
rename,
lambdaFormation,
lambdaEquality
Latex:
ForgetGroup \mmember{} Functor(Group;TypeCat)
Date html generated:
2017_01_19-PM-02_57_14
Last ObjectModification:
2017_01_16-AM-00_45_26
Theory : small!categories
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