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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