Nuprl Lemma : type-functor_wf
Functor ∈ 𝕌'
Proof
Definitions occuring in Statement :
type-functor: Functor,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
type-functor: Functor,
member: t ∈ T,
subtype_rel: A ⊆r B,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
equal-wf-T-base,
equal_wf,
compose_wf,
isect_subtype_rel_trivial,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
setEquality,
productEquality,
functionEquality,
universeEquality,
isectEquality,
because_Cache,
cumulativity,
hypothesisEquality,
cut,
applyEquality,
functionExtensionality,
hypothesis,
thin,
lambdaEquality,
sqequalHypSubstitution,
productElimination,
instantiate,
introduction,
extract_by_obid,
isectElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
baseClosed,
independent_isectElimination,
dependent_pairFormation
Latex:
Functor \mmember{} \mBbbU{}'
Date html generated:
2017_10_01-AM-08_28_35
Last ObjectModification:
2017_07_26-PM-04_23_35
Theory : basic
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