Nuprl Lemma : bag-co-restrict-rep
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ∀[n:ℕ]. ((bag-rep(n;x)|¬x) ~ {})
Proof
Definitions occuring in Statement :
bag-co-restrict: (b|¬x),
bag-rep: bag-rep(n;x),
empty-bag: {},
deq: EqDecider(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
member: t ∈ T,
top: Top,
bag-co-restrict: (b|¬x),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
deq: EqDecider(T),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
eqof: eqof(d),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
false: False,
not: ¬A,
nat: ℕ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
bag-rep: bag-rep(n;x),
eq_int: (i =z j),
subtract: n - m,
empty-bag: {},
nil: [],
bag-filter: [x∈b|p[x]],
filter: filter(P;l),
cons: [a / b],
reduce: reduce(f;k;as),
list_ind: list_ind,
bottom: ⊥,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
strict4: strict4(F),
has-value: (a)↓,
squash: ↓T,
decidable: Dec(P)
Lemmas referenced :
bag_filter_cons_lemma,
bool_wf,
eqtt_to_assert,
safe-assert-deq,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
nat_wf,
deq_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
primrec-unroll,
lifting-strict-decide,
top_wf,
has-value_wf_base,
base_wf,
is-exception_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
eq_int_wf,
assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
neg_assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
natural_numberEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
because_Cache,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
applyEquality,
setElimination,
rename,
lambdaFormation,
unionElimination,
equalityElimination,
isectElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
universeEquality,
isect_memberFormation,
intWeakElimination,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
sqequalAxiom,
baseClosed,
callbyvalueDecide,
unionEquality,
sqleReflexivity,
baseApply,
closedConclusion,
decideExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. \mforall{}[n:\mBbbN{}]. ((bag-rep(n;x)|\mneg{}x) \msim{} \{\})
Date html generated:
2018_05_21-PM-09_52_49
Last ObjectModification:
2017_07_26-PM-06_32_06
Theory : bags_2
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