Nuprl Lemma : seq-comp-truncate
∀[T:Type]. ∀[s:sequence(T)]. ∀[f,n:Top]. (f o seq-truncate(s;n) ~ seq-truncate(f o s;n))
Proof
Definitions occuring in Statement :
seq-truncate: seq-truncate(s;n),
seq-comp: f o s,
sequence: sequence(T),
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sequence: sequence(T),
seq-comp: f o s,
seq-truncate: seq-truncate(s;n)
Lemmas referenced :
top_wf,
sequence_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
sqequalAxiom,
because_Cache,
cut,
extract_by_obid,
hypothesis,
isectElimination,
hypothesisEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[s:sequence(T)]. \mforall{}[f,n:Top]. (f o seq-truncate(s;n) \msim{} seq-truncate(f o s;n))
Date html generated:
2018_07_25-PM-01_28_50
Last ObjectModification:
2018_06_12-AM-10_50_12
Theory : arithmetic
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