Nuprl Lemma : rep-seq-from_wf
∀[T:Type]. ∀[n:ℕ]. ∀[s:ℕn ⟶ T]. ∀[f:ℕ ⟶ T]. (rep-seq-from(s;n;f) ∈ ℕ ⟶ T)
Proof
Definitions occuring in Statement :
rep-seq-from: rep-seq-from(s;n;f),
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,
rep-seq-from: rep-seq-from(s;n;f),
nat: ℕ,
less_than: a < b,
and: P ∧ Q,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
top: Top,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k
Lemmas referenced :
less_than_wf,
int_seg_wf,
lelt_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
because_Cache,
hypothesis,
lessCases,
independent_pairFormation,
isectElimination,
baseClosed,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
hypothesisEquality,
axiomSqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
imageElimination,
productElimination,
extract_by_obid,
independent_functionElimination,
applyEquality,
functionExtensionality,
dependent_set_memberEquality,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:\mBbbN{}n {}\mrightarrow{} T]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} T]. (rep-seq-from(s;n;f) \mmember{} \mBbbN{} {}\mrightarrow{} T)
Date html generated:
2019_06_20-PM-02_56_52
Last ObjectModification:
2018_08_20-PM-09_38_45
Theory : continuity
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