Nuprl Lemma : mset_count_inj
∀s:DSet. ∀a,x:|s|. ((x #∈ mset_inj{s}(a)) = b2i(a (=b) x) ∈ ℤ)
Proof
Definitions occuring in Statement :
mset_inj: mset_inj{s}(x),
mset_count: x #∈ a,
b2i: b2i(b),
infix_ap: x f y,
all: ∀x:A. B[x],
int: ℤ,
equal: s = t ∈ T,
dset: DSet,
set_eq: =b,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
mk_mset: mk_mset(as),
mset_inj: mset_inj{s}(x),
mset_count: x #∈ a,
top: Top,
decidable: Dec(P),
or: P ∨ Q,
infix_ap: x f y,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ
Lemmas referenced :
set_car_wf,
dset_wf,
count_cons_lemma,
istype-void,
count_nil_lemma,
decidable__equal_int,
b2i_wf,
set_eq_wf,
full-omega-unsat,
intformnot_wf,
intformeq_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
inhabitedIsType,
hypothesisEquality,
universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
sqequalRule,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
because_Cache,
unionElimination,
applyEquality,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality
Latex:
\mforall{}s:DSet. \mforall{}a,x:|s|. ((x \#\mmember{} mset\_inj\{s\}(a)) = b2i(a (=\msubb{}) x))
Date html generated:
2019_10_16-PM-01_06_38
Last ObjectModification:
2018_10_08-PM-00_09_10
Theory : mset
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