Nuprl Lemma : int_seg_finite
∀n,m:ℤ. finite({n..m-})
Proof
Definitions occuring in Statement :
finite: finite(T),
int_seg: {i..j-},
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
lelt: i ≤ j < k,
int_seg: {i..j-},
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
less_than': less_than'(a;b),
le: A ≤ B,
prop: ℙ,
and: P ∧ Q,
top: Top,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
nat: ℕ,
exists: ∃x:A. B[x],
or: P ∨ Q,
decidable: Dec(P),
member: t ∈ T,
all: ∀x:A. B[x],
finite: finite(T)
Lemmas referenced :
int_formula_prop_less_lemma,
intformless_wf,
int_seg_properties,
equipollent-zero,
int_seg_wf,
equipollent_wf,
equipollent_interval,
istype-le,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
subtract_wf,
istype-int,
decidable__le
Rules used in proof :
productElimination,
rename,
setElimination,
Error :universeIsType,
independent_pairFormation,
voidElimination,
Error :isect_memberEquality_alt,
int_eqEquality,
Error :lambdaEquality_alt,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
natural_numberEquality,
isectElimination,
Error :dependent_set_memberEquality_alt,
Error :dependent_pairFormation_alt,
Error :inhabitedIsType,
unionElimination,
hypothesis,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
Error :lambdaFormation_alt,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}n,m:\mBbbZ{}. finite(\{n..m\msupminus{}\})
Date html generated:
2019_06_20-PM-02_18_54
Last ObjectModification:
2019_06_19-PM-06_19_45
Theory : equipollence!!cardinality!
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