Nuprl Lemma : map_cons_lemma
∀b,a,f:Top. (map(f;[a / b]) ~ [f a / map(f;b)])
Proof
Definitions occuring in Statement :
map: map(f;as),
cons: [a / b],
top: Top,
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
map: map(f;as),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
top_wf,
list_ind_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}b,a,f:Top. (map(f;[a / b]) \msim{} [f a / map(f;b)])
Date html generated:
2016_05_14-AM-06_28_25
Last ObjectModification:
2015_12_26-PM-00_40_51
Theory : list_0
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