Nuprl Lemma : bool-cardinality-le
|š¹| ā¤ 2
Proof
Definitions occuring in Statement :
cardinality-le: |T| ā¤ n
,
bool: š¹
,
natural_number: $n
Definitions unfolded in proof :
uall: ā[x:A]. B[x]
,
member: t ā T
,
all: āx:A. B[x]
,
implies: P
ā Q
,
length: ||as||
,
list_ind: list_ind,
cons: [a / b]
,
nil: []
,
it: ā
,
bool: š¹
,
unit: Unit
,
btrue: tt
,
uiff: uiff(P;Q)
,
and: P ā§ Q
,
uimplies: b supposing a
,
l_member: (x ā l)
,
exists: āx:A. B[x]
,
nat: ā
,
le: A ā¤ B
,
less_than': less_than'(a;b)
,
not: Ā¬A
,
false: False
,
select: L[n]
,
cand: A cā§ B
,
less_than: a < b
,
squash: āT
,
true: True
,
ge: i ā„ j
,
decidable: Dec(P)
,
or: P āØ Q
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
prop: ā
,
bfalse: ff
,
sq_type: SQType(T)
,
guard: {T}
,
bnot: Ā¬bb
,
ifthenelse: if b then t else f fi
,
assert: āb
,
subtract: n - m
Lemmas referenced :
list-cardinality-le,
bool_wf,
cons_wf,
btrue_wf,
bfalse_wf,
nil_wf,
eqtt_to_assert,
istype-void,
istype-le,
length_of_cons_lemma,
length_of_nil_lemma,
istype-less_than,
length_wf,
select_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
independent_functionElimination,
sqequalRule,
lambdaFormation_alt,
hypothesisEquality,
inhabitedIsType,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation_alt,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
voidElimination,
Error :memTop,
imageMemberEquality,
baseClosed,
productIsType,
setElimination,
rename,
equalityIstype,
because_Cache,
approximateComputation,
lambdaEquality_alt,
int_eqEquality,
universeIsType,
sqequalBase,
equalitySymmetry,
equalityTransitivity,
promote_hyp,
instantiate,
cumulativity
Latex:
|\mBbbB{}| \mleq{} 2
Date html generated:
2020_05_19-PM-09_43_31
Last ObjectModification:
2019_12_31-PM-00_28_25
Theory : list_1
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