Nuprl Lemma : type-cat_wf
TypeCat ∈ SmallCategory'
Proof
Definitions occuring in Statement :
type-cat: TypeCat,
small-category: SmallCategory,
member: t ∈ T
Definitions unfolded in proof :
type-cat: TypeCat,
member: t ∈ T,
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
compose: f o g,
spreadn: spread4,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
compose_wf,
equal_wf,
squash_wf,
true_wf,
eta_conv,
iff_weakening_equal,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_set_memberEquality,
dependent_pairEquality,
universeEquality,
lambdaEquality,
cumulativity,
functionEquality,
hypothesisEquality,
sqequalRule,
independent_pairEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionExtensionality,
applyEquality,
hypothesis,
productEquality,
lambdaFormation,
imageElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
independent_pairFormation,
instantiate
Latex:
TypeCat \mmember{} SmallCategory'
Date html generated:
2017_10_05-AM-00_46_38
Last ObjectModification:
2017_07_28-AM-09_19_32
Theory : small!categories
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