Nuprl Lemma : seq-comp-item
∀[T:Type]. ∀[s:sequence(T)]. ∀[f,i:Top]. (f o s[i] ~ f s[i])
Proof
Definitions occuring in Statement :
seq-comp: f o s,
seq-item: s[i],
sequence: sequence(T),
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sequence: sequence(T),
seq-item: s[i],
seq-comp: f o s,
pi2: snd(t)
Lemmas referenced :
top_wf,
sequence_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesis,
sqequalAxiom,
extract_by_obid,
isect_memberEquality,
isectElimination,
hypothesisEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[s:sequence(T)]. \mforall{}[f,i:Top]. (f o s[i] \msim{} f s[i])
Date html generated:
2018_07_25-PM-01_28_28
Last ObjectModification:
2018_06_11-PM-04_24_58
Theory : arithmetic
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