Nuprl Lemma : remove_repeats_cons_lemma
∀v,u,eq:Top. (remove-repeats(eq;[u / v]) ~ [u / filter(λx.(¬b(eq x u));remove-repeats(eq;v))])
Proof
Definitions occuring in Statement :
remove-repeats: remove-repeats(eq;L),
filter: filter(P;l),
cons: [a / b],
bnot: ¬bb,
top: Top,
all: ∀x:A. B[x],
apply: f a,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
remove-repeats: remove-repeats(eq;L),
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{}v,u,eq:Top. (remove-repeats(eq;[u / v]) \msim{} [u / filter(\mlambda{}x.(\mneg{}\msubb{}(eq x u));remove-repeats(eq;v))])
Date html generated:
2016_05_14-PM-03_26_34
Last ObjectModification:
2015_12_26-PM-06_23_07
Theory : decidable!equality
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