Nuprl Lemma : concat-lifting-3-strict
∀[f:Top]. ∀[b:bag(Top)].
∀b':bag(Top)
((concat-lifting-3(f) {} b b' ~ {}) ∧ (concat-lifting-3(f) b {} b' ~ {}) ∧ (concat-lifting-3(f) b b' {} ~ {}))
Proof
Definitions occuring in Statement :
concat-lifting-3: concat-lifting-3(f),
empty-bag: {},
bag: bag(T),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
and: P ∧ Q,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
concat-lifting-3: concat-lifting-3(f),
concat-lifting: concat-lifting(n;f;bags),
concat-lifting-list: concat-lifting-list(n;bags),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
lifting-gen: lifting-gen(n;f),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
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,
bag_union_empty_lemma,
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,
lambdaFormation,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
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)].
\mforall{}b':bag(Top)
((concat-lifting-3(f) \{\} b b' \msim{} \{\})
\mwedge{} (concat-lifting-3(f) b \{\} b' \msim{} \{\})
\mwedge{} (concat-lifting-3(f) b b' \{\} \msim{} \{\}))
Date html generated:
2016_05_15-PM-03_08_37
Last ObjectModification:
2016_01_16-AM-08_35_53
Theory : bags
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