Nuprl Lemma : for_hdtl_cons_lemma
∀g,as,a,k,f,T:Top. (ForHdTl{T,f,k} h::t ∈ [a / as]. g[h;t] ~ f g[a;as] (ForHdTl{T,f,k} h::t ∈ as. g[h;t]))
Proof
Definitions occuring in Statement :
for_hdtl: ForHdTl{A,f,k} h::t ∈ as. g[h; t],
cons: [a / b],
top: Top,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
for_hdtl: ForHdTl{A,f,k} h::t ∈ as. g[h; t],
top: Top
Lemmas referenced :
top_wf,
mapcons_cons_lemma,
reduce_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{}g,as,a,k,f,T:Top.
(ForHdTl\{T,f,k\} h::t \mmember{} [a / as]. g[h;t] \msim{} f g[a;as] (ForHdTl\{T,f,k\} h::t \mmember{} as. g[h;t]))
Date html generated:
2016_05_14-AM-07_38_36
Last ObjectModification:
2015_12_26-PM-02_12_48
Theory : list_1
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