Nuprl Lemma : finite-type-int_seg
∀i,j:ℤ. finite-type({i..j-})
Proof
Definitions occuring in Statement :
finite-type: finite-type(T),
int_seg: {i..j-},
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
finite-type: finite-type(T),
cardinality-le: |T| ≤ n,
member: t ∈ T,
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
prop: ℙ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
le: A ≤ B,
less_than': less_than'(a;b)
Lemmas referenced :
int_seg-cardinality-le,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
subtract_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
false_wf,
cardinality-le_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
dependent_pairFormation,
isectElimination,
hypothesis,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
dependent_set_memberEquality,
natural_numberEquality,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination
Latex:
\mforall{}i,j:\mBbbZ{}. finite-type(\{i..j\msupminus{}\})
Date html generated:
2017_04_17-AM-07_45_37
Last ObjectModification:
2017_02_27-PM-04_17_17
Theory : list_1
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