Nuprl Lemma : constant-type-functor_wf
∀[X:Type]. (constant-type-functor(X) ∈ Functor)
Proof
Definitions occuring in Statement :
constant-type-functor: constant-type-functor(X),
type-functor: Functor,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
constant-type-functor: constant-type-functor(X),
type-functor: Functor,
member: t ∈ T,
top: Top,
compose: f o g,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
exists: ∃x:A. B[x]
Lemmas referenced :
top_wf,
all_wf,
equal-wf-T-base,
equal_wf,
isect_subtype_rel_trivial,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
dependent_set_memberEquality,
dependent_pairEquality,
lambdaEquality,
cumulativity,
hypothesisEquality,
universeEquality,
isect_memberEquality,
sqequalHypSubstitution,
sqequalRule,
applyEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
voidElimination,
voidEquality,
functionEquality,
isectEquality,
functionExtensionality,
lambdaFormation,
independent_pairFormation,
because_Cache,
productElimination,
thin,
productEquality,
instantiate,
isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
baseClosed,
independent_isectElimination,
dependent_pairFormation
Latex:
\mforall{}[X:Type]. (constant-type-functor(X) \mmember{} Functor)
Date html generated:
2017_10_01-AM-08_28_38
Last ObjectModification:
2017_07_26-PM-04_23_37
Theory : basic
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