Nuprl Lemma : star-append_wf
∀[T:Type]. ∀[P,Q:(T List) ⟶ ℙ]. (star-append(T;P;Q) ∈ (T List) ⟶ ℙ)
Proof
Definitions occuring in Statement :
star-append: star-append(T;P;Q),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
star-append: star-append(T;P;Q),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
all: ∀x:A. B[x],
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
exists_wf,
list_wf,
l_all_wf2,
l_member_wf,
equal_wf,
append_wf,
concat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
productEquality,
lambdaFormation,
setElimination,
rename,
applyEquality,
functionExtensionality,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[P,Q:(T List) {}\mrightarrow{} \mBbbP{}]. (star-append(T;P;Q) \mmember{} (T List) {}\mrightarrow{} \mBbbP{})
Date html generated:
2018_05_21-PM-07_33_40
Last ObjectModification:
2017_07_26-PM-05_08_32
Theory : general
Home
Index