Nuprl Lemma : member-bag-rep
∀[T:Type]. ∀[n:ℕ]. ∀[x,y:T]. y = x ∈ T supposing y ↓∈ bag-rep(n;x)
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
bag-rep: bag-rep(n;x),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
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,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
bag-rep: bag-rep(n;x),
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
uiff: uiff(P;Q),
primrec: primrec(n;b;c),
empty-bag: {},
nil: [],
it: ⋅,
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff,
sq_or: a ↓∨ b,
squash: ↓T,
bool: 𝔹,
unit: Unit,
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T
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,
bag-member_wf,
bag-rep_wf,
list-subtype-bag,
primrec-unroll,
bag-member-empty-iff,
empty-bag_wf,
nil_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
eq_int_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
iff_transitivity,
assert_wf,
bnot_wf,
not_wf,
equal-wf-base,
int_subtype_base,
iff_weakening_uiff,
assert_of_bnot,
bag-member-cons,
primrec_wf,
bag_wf,
le_wf,
cons-bag_wf,
int_seg_wf,
equal_wf,
bool_cases_sqequal,
assert-bnot,
neg_assert_of_eq_int,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
cumulativity,
because_Cache,
applyEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
unionElimination,
instantiate,
promote_hyp,
baseClosed,
impliesFunctionality,
dependent_set_memberEquality,
imageElimination,
equalityElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[x,y:T]. y = x supposing y \mdownarrow{}\mmember{} bag-rep(n;x)
Date html generated:
2017_10_01-AM-08_54_58
Last ObjectModification:
2017_07_26-PM-04_36_49
Theory : bags
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