Nuprl Lemma : repn_wf
∀[T:Type]. ∀[x:T]. ∀[n:ℕ]. (repn(n;x) ∈ {z:T| z = x ∈ T} List)
Proof
Definitions occuring in Statement :
repn: repn(n;x),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
repn: repn(n;x),
prop: ℙ,
nat: ℕ
Lemmas referenced :
primrec_wf,
list_wf,
equal_wf,
nil_wf,
cons_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality,
dependent_set_memberEquality,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[n:\mBbbN{}]. (repn(n;x) \mmember{} \{z:T| z = x\} List)
Date html generated:
2017_04_17-AM-07_49_41
Last ObjectModification:
2017_02_27-PM-04_23_28
Theory : list_1
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