Nuprl Lemma : union-list2-simplify1
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[ll:T List List]. ∀[L:T List].
(union-list2(eq;[L; [L / ll]]) ~ union-list2(eq;[L / ll]))
Proof
Definitions occuring in Statement :
union-list2: union-list2(eq;ll),
cons: [a / b],
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
union-list2: union-list2(eq;ll),
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
ifthenelse: if b then t else f fi ,
bfalse: ff,
uimplies: b supposing a,
l_contains: A ⊆ B,
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
less_than: a < b,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B
Lemmas referenced :
select_member,
l_member_wf,
cons_member,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
select_wf,
member-union-list2,
length_wf,
int_seg_wf,
cons_wf,
union-list2_wf,
l-union-subset,
null_cons_lemma,
list_ind_cons_lemma,
deq_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
universeEquality,
isect_memberFormation,
introduction,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_isectElimination,
lambdaFormation,
natural_numberEquality,
cumulativity,
setElimination,
rename,
productElimination,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
imageElimination,
independent_functionElimination,
inlFormation,
productEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[ll:T List List]. \mforall{}[L:T List].
(union-list2(eq;[L; [L / ll]]) \msim{} union-list2(eq;[L / ll]))
Date html generated:
2016_05_14-PM-03_25_30
Last ObjectModification:
2016_01_14-PM-11_22_23
Theory : decidable!equality
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