Nuprl Lemma : ss-cat_wf
ss-cat{i:l}() ∈ SmallCategory'
Proof
Definitions occuring in Statement :
ss-cat: ss-cat{i:l}(),
small-category: SmallCategory,
member: t ∈ T
Definitions unfolded in proof :
guard: {T},
compose: f o g,
cand: A c∧ B,
and: P ∧ Q,
uimplies: b supposing a,
so_apply: x[s1;s2;s3;s4;s5],
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
ss-map: ss-map(X;Y;f),
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
uall: ∀[x:A]. B[x],
member: t ∈ T,
ss-cat: ss-cat{i:l}()
Lemmas referenced :
comp_assoc,
set_wf,
compose_wf,
ss-sep_wf,
ss-map_wf,
ss-point_wf,
separation-space_wf,
mk-cat_wf
Rules used in proof :
independent_functionElimination,
dependent_functionElimination,
independent_pairFormation,
equalitySymmetry,
independent_isectElimination,
rename,
setElimination,
lambdaFormation,
dependent_set_memberEquality,
functionExtensionality,
because_Cache,
universeEquality,
cumulativity,
applyEquality,
hypothesisEquality,
functionEquality,
setEquality,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
instantiate,
cut,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
ss-cat\{i:l\}() \mmember{} SmallCategory'
Date html generated:
2018_07_29-AM-10_10_46
Last ObjectModification:
2018_06_28-PM-03_34_33
Theory : constructive!algebra
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