Nuprl Lemma : type-functor-product_wf
∀[F,G:Functor]. (F * G ∈ Functor)
Proof
Definitions occuring in Statement :
type-functor-product: p * 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-product: p * q,
and: P ∧ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
compose: f o g,
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
implies: P ⇒ Q,
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 :
istype-universe,
equal_wf,
squash_wf,
true_wf,
trivial-equal,
iff_weakening_equal,
subtype_rel_self,
isect_subtype_rel_trivial,
subtype_rel_universe1,
subtype_rel_wf,
type-functor_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
dependent_set_memberEquality_alt,
dependent_pairEquality_alt,
lambdaEquality_alt,
because_Cache,
universeIsType,
universeEquality,
isect_memberEquality_alt,
independent_pairEquality,
lambdaFormation_alt,
applyEquality,
hypothesisEquality,
hypothesis,
functionIsType,
inhabitedIsType,
dependent_functionElimination,
productIsType,
introduction,
extract_by_obid,
isectElimination,
isectIsType,
imageElimination,
equalityTransitivity,
equalitySymmetry,
productEquality,
equalityIsType1,
independent_functionElimination,
independent_pairFormation,
equalityIsType3,
baseClosed,
applyLambdaEquality,
functionExtensionality,
natural_numberEquality,
imageMemberEquality,
independent_isectElimination,
instantiate,
cumulativity,
functionEquality,
isectEquality,
closedConclusion,
dependent_pairFormation_alt
Latex:
\mforall{}[F,G:Functor]. (F * G \mmember{} Functor)
Date html generated:
2019_10_15-AM-10_47_03
Last ObjectModification:
2018_10_11-PM-06_49_58
Theory : basic
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