Nuprl Lemma : reduce2_cons_lemma
∀t,h,i,k,f:Top. (reduce2(f;k;i;[h / t]) ~ f h i reduce2(f;k;i + 1;t))
Proof
Definitions occuring in Statement :
reduce2: reduce2(f;k;i;as),
cons: [a / b],
top: Top,
all: ∀x:A. B[x],
apply: f a,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
reduce2: reduce2(f;k;i;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{}t,h,i,k,f:Top. (reduce2(f;k;i;[h / t]) \msim{} f h i reduce2(f;k;i + 1;t))
Date html generated:
2016_05_15-PM-01_56_36
Last ObjectModification:
2015_12_27-AM-00_25_03
Theory : list!
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