Nuprl Lemma : lifting-2-strict
∀[f:Top]. ∀[b:bag(Top)].  ((lifting-2(f) {} b ~ {}) ∧ (lifting-2(f) b {} ~ {}))
Proof
Definitions occuring in Statement : 
lifting-2: lifting-2(f)
, 
empty-bag: {}
, 
bag: bag(T)
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
and: P ∧ Q
, 
apply: f a
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
nat: ℕ
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
lifting-2: lifting-2(f)
, 
lifting2: lifting2(f;abag;bbag)
, 
lifting-gen: lifting-gen(n;f)
, 
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
, 
less_than: a < b
, 
squash: ↓T
, 
true: True
, 
empty-bag: {}
, 
bag-null: bag-null(bs)
, 
select: L[n]
, 
cons: [a / b]
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
subtype_rel: A ⊆r B
, 
subtract: n - m
Lemmas referenced : 
list_wf, 
bag-subtype-list, 
list-subtype-bag, 
null_wf, 
assert_wf, 
null_nil_lemma, 
lelt_wf, 
int_seg_wf, 
int_term_value_add_lemma, 
int_formula_prop_less_lemma, 
itermAdd_wf, 
intformless_wf, 
decidable__lt, 
length_of_nil_lemma, 
length_of_cons_lemma, 
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, 
nil_wf, 
empty-bag_wf, 
cons_wf, 
top_wf, 
bag_wf, 
select_wf, 
le_wf, 
false_wf, 
lifting-gen-strict
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
dependent_set_memberEquality, 
natural_numberEquality, 
sqequalRule, 
independent_pairFormation, 
lambdaFormation, 
hypothesis, 
hypothesisEquality, 
lambdaEquality, 
because_Cache, 
setElimination, 
rename, 
independent_isectElimination, 
productElimination, 
dependent_functionElimination, 
unionElimination, 
dependent_pairFormation, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
computeAll, 
addEquality, 
independent_pairEquality, 
sqequalAxiom, 
imageMemberEquality, 
baseClosed, 
applyEquality
Latex:
\mforall{}[f:Top].  \mforall{}[b:bag(Top)].    ((lifting-2(f)  \{\}  b  \msim{}  \{\})  \mwedge{}  (lifting-2(f)  b  \{\}  \msim{}  \{\}))
Date html generated:
2016_05_15-PM-03_02_07
Last ObjectModification:
2016_01_16-AM-08_36_35
Theory : bags
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