Nuprl Lemma : mklist_wf
∀[T:Type]. ∀[n:ℕ]. ∀[f:ℕn ⟶ T]. (mklist(n;f) ∈ T List)
Proof
Definitions occuring in Statement :
mklist: mklist(n;f),
list: T List,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mklist: mklist(n;f),
nat: ℕ
Lemmas referenced :
primrec_wf,
list_wf,
nil_wf,
append_wf,
cons_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
natural_numberEquality,
setElimination,
rename,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :universeIsType,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[f:\mBbbN{}n {}\mrightarrow{} T]. (mklist(n;f) \mmember{} T List)
Date html generated:
2019_06_20-PM-01_31_04
Last ObjectModification:
2018_09_26-PM-05_51_05
Theory : list_1
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