Nuprl Lemma : RankEx2_UnionList_wf
∀[S,T:Type]. ∀[unionlist:T + (RankEx2(S;T) List)]. (RankEx2_UnionList(unionlist) ∈ RankEx2(S;T))
Proof
Definitions occuring in Statement :
RankEx2_UnionList: RankEx2_UnionList(unionlist),
RankEx2: RankEx2(S;T),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
RankEx2: RankEx2(S;T),
RankEx2_UnionList: RankEx2_UnionList(unionlist),
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
ext-eq: A ≡ B,
RankEx2co_size: RankEx2co_size(p),
RankEx2_size: RankEx2_size(p),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
less_than: a < b,
squash: ↓T,
so_apply: x[s]
Lemmas referenced :
RankEx2co_size_wf,
has-value_wf-partial,
int-value-type,
set-value-type,
value-type-has-value,
nat_wf,
int_seg_wf,
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,
length_wf,
int_seg_properties,
select_wf,
RankEx2_size_wf,
length_wf_nat,
sum-nat,
le_wf,
false_wf,
add_nat_wf,
assert_of_eq_atom,
eqtt_to_assert,
neg_assert_of_eq_atom,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
bool_wf,
eq_atom_wf,
subtype_rel_list,
RankEx2co_wf,
RankEx2_wf,
list_wf,
subtype_rel_union,
RankEx2co-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
dependent_set_memberEquality,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
dependent_pairEquality,
tokenEquality,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
setElimination,
rename,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
productEquality,
unionEquality,
voidEquality,
equalityEquality,
natural_numberEquality,
independent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
computeAll,
imageElimination,
universeEquality
Latex:
\mforall{}[S,T:Type]. \mforall{}[unionlist:T + (RankEx2(S;T) List)]. (RankEx2\_UnionList(unionlist) \mmember{} RankEx2(S;T))
Date html generated:
2016_05_16-AM-09_00_30
Last ObjectModification:
2016_01_17-AM-09_41_22
Theory : C-semantics
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