Nuprl Lemma : remove-repeats-fun_wf
∀[A,B:Type]. ∀[eq:EqDecider(B)]. ∀[f:A ⟶ B]. ∀[L:A List]. (remove-repeats-fun(eq;f;L) ∈ A List)
Proof
Definitions occuring in Statement :
remove-repeats-fun: remove-repeats-fun(eq;f;L),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
remove-repeats-fun: remove-repeats-fun(eq;f;L),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
deq: EqDecider(T),
prop: ℙ,
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_wf,
list_wf,
nil_wf,
cons_wf,
filter_wf5,
bnot_wf,
l_member_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
setElimination,
rename,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[eq:EqDecider(B)]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[L:A List]. (remove-repeats-fun(eq;f;L) \mmember{} A List)
Date html generated:
2016_05_14-PM-03_28_21
Last ObjectModification:
2015_12_26-PM-06_23_53
Theory : decidable!equality
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