Nuprl Lemma : polyvar_wf
∀[v:ℕ]. (polyvar(v) ∈ polynom(v + 1))
Proof
Definitions occuring in Statement : 
polyvar: polyvar(v)
, 
polynom: polynom(n)
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
add: n + m
, 
natural_number: $n
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
nat: ℕ
, 
implies: P 
⇒ Q
, 
false: False
, 
ge: i ≥ j 
, 
uimplies: b supposing a
, 
not: ¬A
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
all: ∀x:A. B[x]
, 
top: Top
, 
and: P ∧ Q
, 
prop: ℙ
, 
polynom: polynom(n)
, 
polyvar: polyvar(v)
, 
cand: A c∧ B
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
iff: P 
⇐⇒ Q
, 
poly-zero: poly-zero(p)
, 
band: p ∧b q
, 
tree_leaf?: tree_leaf?(v)
, 
eq_atom: x =a y
, 
pi1: fst(t)
, 
tree_node: tree_node(left;right)
, 
rev_implies: P 
⇐ Q
, 
poly-int: poly-int(p)
, 
tree_ind: tree_ind, 
tree_leaf: tree_leaf(value)
, 
btrue: tt
, 
eq_int: (i =z j)
, 
tree_leaf-value: tree_leaf-value(v)
, 
pi2: snd(t)
, 
ispolyform: ispolyform(p)
, 
lt_int: i <z j
, 
true: True
, 
polyform: polyform(n)
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
uiff: uiff(P;Q)
, 
subtype_rel: A ⊆r B
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
nequal: a ≠ b ∈ T 
, 
has-value: (a)↓
, 
subtract: n - m
, 
decidable: Dec(P)
, 
squash: ↓T
Lemmas referenced : 
nat_properties, 
full-omega-unsat, 
intformand_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_wf, 
intformless_wf, 
istype-int, 
int_formula_prop_and_lemma, 
istype-void, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_less_lemma, 
int_formula_prop_wf, 
ge_wf, 
istype-less_than, 
iff_imp_equal_bool, 
poly-zero_wf, 
tree_node_wf, 
tree_leaf_wf, 
bfalse_wf, 
istype-assert, 
poly-int_wf, 
assert_elim, 
btrue_neq_bfalse, 
ispolyform_wf, 
tree_leaf?_wf, 
bool_wf, 
subtract-1-ge-0, 
eq_int_wf, 
eqtt_to_assert, 
assert_of_eq_int, 
subtract-add-cancel, 
intformeq_wf, 
int_formula_prop_eq_lemma, 
eqff_to_assert, 
int_subtype_base, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_int, 
value-type-has-value, 
polyform_wf, 
value-type-polyform, 
nat_wf, 
ispolyform_node_lemma, 
ispolyform_leaf_lemma, 
iff_transitivity, 
assert_wf, 
subtract_wf, 
btrue_wf, 
lt_int_wf, 
assert_of_lt_int, 
iff_weakening_uiff, 
less_than_wf, 
add-subtract-cancel, 
intformnot_wf, 
itermAdd_wf, 
int_formula_prop_not_lemma, 
int_term_value_add_lemma, 
true_wf, 
assert_of_band, 
add-associates, 
add-swap, 
add-commutes, 
zero-add, 
decidable__lt, 
assert_functionality_wrt_uiff, 
band_wf, 
squash_wf, 
iff_functionality_wrt_iff, 
false_wf, 
iff_weakening_equal, 
equal_wf, 
istype-universe, 
subtype_rel_self
Rules used in proof : 
cut, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
setElimination, 
rename, 
intWeakElimination, 
lambdaFormation_alt, 
natural_numberEquality, 
independent_isectElimination, 
approximateComputation, 
independent_functionElimination, 
dependent_pairFormation_alt, 
lambdaEquality_alt, 
int_eqEquality, 
dependent_functionElimination, 
isect_memberEquality_alt, 
voidElimination, 
sqequalRule, 
independent_pairFormation, 
universeIsType, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionIsTypeImplies, 
inhabitedIsType, 
intEquality, 
because_Cache, 
dependent_set_memberEquality_alt, 
productElimination, 
applyEquality, 
functionIsType, 
productIsType, 
equalityIsType3, 
baseClosed, 
closedConclusion, 
unionElimination, 
equalityElimination, 
int_eqReduceTrueSq, 
equalityIsType2, 
baseApply, 
promote_hyp, 
instantiate, 
cumulativity, 
int_eqReduceFalseSq, 
callbyvalueReduce, 
axiomSqleEquality, 
equalityIsType1, 
addEquality, 
productEquality, 
imageElimination, 
imageMemberEquality, 
universeEquality
Latex:
\mforall{}[v:\mBbbN{}].  (polyvar(v)  \mmember{}  polynom(v  +  1))
Date html generated:
2019_10_15-AM-10_52_16
Last ObjectModification:
2018_10_12-AM-10_36_37
Theory : integer!polynomial!trees
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