Nuprl Lemma : select_upto
∀[m:ℕ]. ∀[n:ℕm]. (upto(m)[n] = n ∈ ℤ)
Proof
Definitions occuring in Statement :
upto: upto(n),
select: L[n],
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
upto: upto(n),
nat: ℕ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtract: n - m,
int_seg: {i..j-},
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
nat_wf,
int_seg_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermVar_wf,
itermConstant_wf,
itermAdd_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_properties,
int_seg_properties,
add-zero,
minus-zero,
int_subtype_base,
set_subtype_base,
subtype_base_sq,
select-from-upto
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
applyEquality,
lambdaEquality,
instantiate,
because_Cache,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
productElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality
Latex:
\mforall{}[m:\mBbbN{}]. \mforall{}[n:\mBbbN{}m]. (upto(m)[n] = n)
Date html generated:
2016_05_14-PM-02_04_20
Last ObjectModification:
2016_01_15-AM-08_04_54
Theory : list_1
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