Nuprl Lemma : lifting2_wf
∀[A,B,C:Type]. ∀[f:A ⟶ B ⟶ C]. ∀[abag:bag(A)]. ∀[bbag:bag(B)]. (lifting2(f;abag;bbag) ∈ bag(C))
Proof
Definitions occuring in Statement :
lifting2: lifting2(f;abag;bbag),
bag: bag(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,
lifting2: lifting2(f;abag;bbag),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
sq_type: SQType(T),
select: L[n],
cons: [a / b],
subtract: n - m,
subtype_rel: A ⊆r B,
funtype: funtype(n;A;T),
primrec: primrec(n;b;c)
Lemmas referenced :
lifting-gen-rev_wf,
false_wf,
le_wf,
select_wf,
cons_wf,
nil_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
length_of_cons_lemma,
length_of_nil_lemma,
decidable__lt,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_seg_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
int_seg_subtype,
int_seg_cases,
subtype_rel_self,
funtype_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
lambdaEquality,
instantiate,
universeEquality,
because_Cache,
cumulativity,
setElimination,
rename,
independent_isectElimination,
productElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
addEquality,
equalityTransitivity,
equalitySymmetry,
hypothesis_subsumption,
applyEquality,
axiomEquality,
functionEquality
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[abag:bag(A)]. \mforall{}[bbag:bag(B)]. (lifting2(f;abag;bbag) \mmember{} bag(C))
Date html generated:
2018_05_21-PM-06_26_19
Last ObjectModification:
2018_05_19-PM-05_15_57
Theory : bags
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