Nuprl Lemma : lifting-gen-strict
∀[n:ℕ]. ∀[f:Top]. ∀[a:k:ℕn ⟶ bag(Top)]. lifting-gen(n;f) a ~ {} supposing ∃k:ℕn. (↑bag-null(a k))
Proof
Definitions occuring in Statement :
lifting-gen: lifting-gen(n;f),
bag-null: bag-null(bs),
empty-bag: {},
bag: bag(T),
int_seg: {i..j-},
nat: ℕ,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
exists: ∃x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
lifting-gen: lifting-gen(n;f),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
le: A ≤ B,
int_seg: {i..j-},
lelt: i ≤ j < k,
so_apply: x[s],
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than': less_than'(a;b)
Lemmas referenced :
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,
exists_wf,
int_seg_wf,
assert_wf,
bag-null_wf,
top_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
lelt_wf,
bag_wf,
le_wf,
subtract_wf,
nat_wf,
int_seg_properties,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
eq_int_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
equal_wf,
eqtt_to_assert,
assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
itermAdd_wf,
int_term_value_add_lemma,
decidable__equal_int,
bag-combine-empty-left,
bag-combine-empty-right,
decidable__lt,
false_wf,
assert-bag-null,
equal-empty-bag
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lambdaFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
because_Cache,
applyEquality,
functionExtensionality,
productElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberFormation,
unionElimination,
equalityElimination,
baseClosed,
impliesFunctionality,
addEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f:Top]. \mforall{}[a:k:\mBbbN{}n {}\mrightarrow{} bag(Top)]. lifting-gen(n;f) a \msim{} \{\} supposing \mexists{}k:\mBbbN{}n. (\muparrow{}bag-null(a k))
Date html generated:
2017_10_01-AM-09_03_01
Last ObjectModification:
2017_07_26-PM-04_44_01
Theory : bags
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