Nuprl Lemma : imax-list-cons-is-nat
∀L:ℤ List. ∀[x:ℕ]. (imax-list([x / L]) ∈ ℕ)
Proof
Definitions occuring in Statement :
imax-list: imax-list(L),
cons: [a / b],
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
uimplies: b supposing a,
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
false: False,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
l_exists: (∃x∈L. P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than': less_than'(a;b),
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
true: True,
guard: {T},
uiff: uiff(P;Q),
select: L[n],
cons: [a / b]
Lemmas referenced :
imax-list_wf,
length_of_cons_lemma,
non_neg_length,
nat_properties,
decidable__lt,
length_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
imax-list-ub,
cons_wf,
le_wf,
nat_wf,
list_wf,
false_wf,
add_nat_plus,
length_wf_nat,
less_than_wf,
nat_plus_wf,
nat_plus_properties,
add-is-int-iff,
intformeq_wf,
int_formula_prop_eq_lemma,
equal_wf,
lelt_wf,
decidable__le,
select_wf,
int_seg_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_isectElimination,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
intEquality,
hypothesisEquality,
setElimination,
rename,
natural_numberEquality,
addEquality,
unionElimination,
productElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
applyLambdaEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
imageElimination
Latex:
\mforall{}L:\mBbbZ{} List. \mforall{}[x:\mBbbN{}]. (imax-list([x / L]) \mmember{} \mBbbN{})
Date html generated:
2018_05_21-PM-00_32_33
Last ObjectModification:
2018_05_19-AM-06_42_36
Theory : list_1
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