Nuprl Lemma : tf-apply_wf
∀[A:Type]. ∀[a:A]. ∀[B:type-function{i:l}(A)]. (tf-apply(B;a) ∈ Type)
Proof
Definitions occuring in Statement :
tf-apply: tf-apply(f;x),
type-function: type-function{i:l}(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
type-function: type-function{i:l}(A),
tf-apply: tf-apply(f;x),
member: t ∈ T,
per-function: per-function(A;a.B[a]),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
base-type-family: base-type-family{i:l}(A;a.B[a]),
implies: P ⇒ Q,
guard: {T},
squash: ↓T,
prop: ℙ,
true: True
Lemmas referenced :
type-function_wf,
istype-universe,
function-eq-implies,
function-eq_wf,
member_wf,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
sqequalHypSubstitution,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeEquality,
pointwiseFunctionality,
sqequalRule,
pertypeElimination,
instantiate,
cumulativity,
baseClosed,
independent_isectElimination,
Error :equalityIsType4,
Error :inhabitedIsType,
Error :isect_memberEquality_alt,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
independent_functionElimination,
applyEquality,
Error :lambdaEquality_alt,
imageElimination,
natural_numberEquality,
imageMemberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[a:A]. \mforall{}[B:type-function\{i:l\}(A)]. (tf-apply(B;a) \mmember{} Type)
Date html generated:
2019_06_20-AM-11_30_01
Last ObjectModification:
2018_10_06-AM-10_08_45
Theory : per!type
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