Nuprl Lemma : type-functor-compose_wf
∀[F,G:Functor]. (F o G ∈ Functor)
Proof
Definitions occuring in Statement :
type-functor-compose: p o q,
type-functor: Functor,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
type-functor: Functor,
type-functor-compose: p o q,
and: P ∧ Q,
compose: f o g,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
cand: A c∧ B,
squash: ↓T,
label: ...$L... t,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
and_wf,
iff_weakening_equal,
all_wf,
equal-wf-T-base,
isect_subtype_rel_trivial,
subtype_rel_wf,
type-functor_wf,
subtype_rel_dep_function,
subtype_rel_weakening,
ext-eq_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
dependent_set_memberEquality,
dependent_pairEquality,
lambdaEquality,
applyEquality,
because_Cache,
cumulativity,
hypothesisEquality,
isect_memberEquality,
isectElimination,
functionExtensionality,
universeEquality,
equalityTransitivity,
equalitySymmetry,
hypothesis,
isectEquality,
functionEquality,
lambdaFormation,
instantiate,
introduction,
extract_by_obid,
dependent_functionElimination,
independent_functionElimination,
imageElimination,
independent_pairFormation,
applyLambdaEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productEquality,
dependent_pairFormation
Latex:
\mforall{}[F,G:Functor]. (F o G \mmember{} Functor)
Date html generated:
2017_10_01-AM-08_28_46
Last ObjectModification:
2017_07_26-PM-04_23_40
Theory : basic
Home
Index