Nuprl Lemma : group-cat_wf
Group ∈ SmallCategory'
Proof
Definitions occuring in Statement :
group-cat: Group,
small-category: SmallCategory,
member: t ∈ T
Definitions unfolded in proof :
group-cat: Group,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
grp: Group{i},
mon: Mon,
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda5,
imon: IMonoid,
prop: ℙ,
so_apply: x[s1;s2;s3;s4;s5],
uimplies: b supposing a,
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
monoid_hom: MonHom(M1,M2),
compose: f o g,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
monoid_hom_p: IsMonHom{M1,M2}(f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f)
Lemmas referenced :
mk-cat_wf,
grp_wf,
monoid_hom_wf,
compose_wf_for_mon_hom,
grp_sig_wf,
monoid_p_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
inverse_wf,
grp_inv_wf,
monoid_hom_properties,
monoid_hom_p_wf,
equal_wf,
compose_wf,
comp_assoc,
iff_weakening_equal,
infix_ap_wf,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
setElimination,
rename,
because_Cache,
hypothesisEquality,
applyEquality,
cumulativity,
universeEquality,
setEquality,
independent_isectElimination,
lambdaFormation,
equalitySymmetry,
dependent_set_memberEquality,
functionExtensionality,
independent_pairFormation,
imageElimination,
functionEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
equalityTransitivity,
productElimination,
independent_functionElimination,
isect_memberFormation,
isect_memberEquality,
axiomEquality
Latex:
Group \mmember{} SmallCategory'
Date html generated:
2020_05_20-AM-07_56_58
Last ObjectModification:
2017_07_28-AM-09_20_28
Theory : small!categories
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