Nuprl Lemma : bool-cardinality-le
|𝔹| ≤ 2
Proof
Definitions occuring in Statement :
cardinality-le: |T| ≤ n,
bool: 𝔹,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
length: ||as||,
list_ind: list_ind,
cons: [a / b],
nil: [],
it: ⋅,
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
false: False,
select: L[n],
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
true: True,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
prop: ℙ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
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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