Nuprl Lemma : seq-truncate_wf
∀[T:Type]. ∀[s:sequence(T)]. ∀[n:ℕ]. seq-truncate(s;n) ∈ sequence(T) supposing n ≤ ||s||
Proof
Definitions occuring in Statement :
seq-truncate: seq-truncate(s;n),
seq-len: ||s||,
sequence: sequence(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
seq-truncate: seq-truncate(s;n),
sequence: sequence(T),
seq-len: ||s||,
pi1: fst(t),
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
le: A ≤ B,
guard: {T}
Lemmas referenced :
subtype_rel_dep_function,
int_seg_wf,
subtype_rel_sets,
and_wf,
le_wf,
less_than_wf,
less_than_transitivity1,
seq-len_wf,
nat_wf,
sequence_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairEquality,
hypothesisEquality,
applyEquality,
extract_by_obid,
isectElimination,
natural_numberEquality,
setElimination,
rename,
hypothesis,
lambdaEquality,
because_Cache,
independent_isectElimination,
intEquality,
setEquality,
lambdaFormation,
independent_pairFormation,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[s:sequence(T)]. \mforall{}[n:\mBbbN{}]. seq-truncate(s;n) \mmember{} sequence(T) supposing n \mleq{} ||s||
Date html generated:
2018_07_25-PM-01_28_37
Last ObjectModification:
2018_06_11-PM-11_29_45
Theory : arithmetic
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