Nuprl Lemma : map-pair
∀[f,a,b:Top]. (map(f;<a, b>) ~ <f a, map(f;b)>)
Proof
Definitions occuring in Statement :
map: map(f;as),
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
cons: [a / b],
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x]
Lemmas referenced :
map_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[f,a,b:Top]. (map(f;<a, b>) \msim{} <f a, map(f;b)>)
Date html generated:
2016_05_14-AM-06_29_20
Last ObjectModification:
2015_12_26-PM-00_40_14
Theory : list_0
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