Nuprl Lemma : oob-apply_wf
∀[A,B:Type]. ∀[X:bag(A)]. ∀[Y:bag(B)]. (oob-apply(X;Y) ∈ bag(one_or_both(A;B)))
Proof
Definitions occuring in Statement :
oob-apply: oob-apply(xs;ys),
one_or_both: one_or_both(A;B),
bag: bag(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
oob-apply: oob-apply(xs;ys),
subtype_rel: A ⊆r B,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
eq_int_wf,
bag-size_wf,
nat_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
single-bag_wf,
one_or_both_wf,
oobboth_wf,
bag-only_wf2,
single-valued-bag-if-le1,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
itermConstant_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
oobleft_wf,
equal_wf,
oobright_wf,
empty-bag_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
because_Cache,
intEquality,
independent_functionElimination,
productElimination,
independent_isectElimination,
dependent_functionElimination,
independent_pairEquality,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
impliesFunctionality,
axiomEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[X:bag(A)]. \mforall{}[Y:bag(B)]. (oob-apply(X;Y) \mmember{} bag(one\_or\_both(A;B)))
Date html generated:
2018_05_21-PM-08_59_48
Last ObjectModification:
2017_07_26-PM-06_23_16
Theory : general
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