Nuprl Lemma : for_cons_lemma
∀g,as,a,k,f,T:Top. (For{T,f,k} x ∈ [a / as]. g[x] ~ f g[a] (For{T,f,k} x ∈ as. g[x]))
Proof
Definitions occuring in Statement :
for: For{T,op,id} x ∈ as. f[x],
cons: [a / b],
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
for: For{T,op,id} x ∈ as. f[x],
top: Top,
tlambda: λx:T. b[x]
Lemmas referenced :
top_wf,
map_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. (For\{T,f,k\} x \mmember{} [a / as]. g[x] \msim{} f g[a] (For\{T,f,k\} x \mmember{} as. g[x]))
Date html generated:
2016_05_14-AM-07_38_21
Last ObjectModification:
2015_12_26-PM-02_12_36
Theory : list_1
Home
Index