Nuprl Lemma : provisional-apply2_wf
∀[A,B,C:Type]. ∀[f:A ⟶ B ⟶ C]. ∀[a:Provisional(A)]. ∀[b:Provisional(B)]. (provisional-apply2(f;a;b) ∈ Provisional(C))
Proof
Definitions occuring in Statement :
provisional-apply2: provisional-apply2(f;a;b),
provisional-type: Provisional(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
provisional-apply2: provisional-apply2(f;a;b),
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
sq_stable: SqStable(P),
implies: P ⇒ Q
Lemmas referenced :
provision_wf,
allowed_wf,
allow_wf,
sq_stable__allowed,
squash_wf,
provisional-type_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
productEquality,
hypothesis,
isect_memberEquality_alt,
applyEquality,
instantiate,
because_Cache,
independent_isectElimination,
imageElimination,
productElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectIsTypeImplies,
inhabitedIsType,
functionIsType,
universeEquality
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[a:Provisional(A)]. \mforall{}[b:Provisional(B)].
(provisional-apply2(f;a;b) \mmember{} Provisional(C))
Date html generated:
2020_05_20-AM-08_01_24
Last ObjectModification:
2020_05_17-PM-08_16_05
Theory : monads
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