Nuprl Lemma : eager_product_map_cons_lemma
∀L,as,a,f:Top. (eager-product-map(f;[a / as];L) ~ eager-map-append(f a;L;eager-product-map(f;as;L)))
Proof
Definitions occuring in Statement :
eager-product-map: eager-product-map(f;as;bs),
eager-map-append: eager-map-append(f;as;bs),
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,
eager-product-map: eager-product-map(f;as;bs),
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{}L,as,a,f:Top.
(eager-product-map(f;[a / as];L) \msim{} eager-map-append(f a;L;eager-product-map(f;as;L)))
Date html generated:
2016_05_14-AM-06_55_43
Last ObjectModification:
2015_12_26-PM-01_15_15
Theory : omega
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