Nuprl Lemma : add-polynom_wf
∀[n:ℕ]. ∀[p,q:polyform(n)]. (add-polynom(p;q) ∈ polyform(n))
Proof
Definitions occuring in Statement :
add-polynom: add-polynom(p;q)
,
polyform: polyform(n)
,
nat: ℕ
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x]
,
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]
,
top: Top
,
and: P ∧ Q
,
prop: ℙ
,
guard: {T}
,
polyform: polyform(n)
,
subtype_rel: A ⊆r B
,
int_seg: {i..j-}
,
lelt: i ≤ j < k
,
decidable: Dec(P)
,
or: P ∨ Q
,
le: A ≤ B
,
less_than': less_than'(a;b)
,
ext-eq: A ≡ B
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
uiff: uiff(P;Q)
,
sq_type: SQType(T)
,
eq_atom: x =a y
,
ifthenelse: if b then t else f fi
,
tree_leaf: tree_leaf(value)
,
assert: ↑b
,
tree_size: tree_size(p)
,
add-polynom: add-polynom(p;q)
,
tree_leaf?: tree_leaf?(v)
,
pi1: fst(t)
,
tree_leaf-value: tree_leaf-value(v)
,
tree_node-left: tree_node-left(v)
,
pi2: snd(t)
,
tree_node-right: tree_node-right(v)
,
bfalse: ff
,
bnot: ¬bb
,
tree_node: tree_node(left;right)
,
less_than: a < b
,
polyconst: polyconst(k)
,
has-value: (a)↓
,
ispolyform: ispolyform(p)
,
tree_ind: tree_ind,
true: True
,
polynom: polynom(n)
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
,
squash: ↓T
,
band: p ∧b q
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
cand: A c∧ B
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
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,
less_than_wf,
le_wf,
tree_size_wf,
polyform_wf,
nat_wf,
int_seg_wf,
int_seg_properties,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
decidable__equal_int,
int_seg_subtype,
false_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
tree-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
ispolyform_leaf_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
ispolyform_node_lemma,
decidable__lt,
lelt_wf,
itermAdd_wf,
int_term_value_add_lemma,
add_nat_wf,
add-is-int-iff,
value-type-has-value,
int-value-type,
polynom_wf,
assert_wf,
ispolyform_wf,
band_wf,
lt_int_wf,
tree_leaf_wf,
set_subtype_base,
int_subtype_base,
value-type-polyform,
tree_wf,
valuetype__tree,
tree_node_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
assert_of_lt_int,
le_weakening2,
poly-zero_wf,
poly-int_wf,
polyform-subtype,
assert_elim
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
addEquality,
applyEquality,
because_Cache,
productElimination,
unionElimination,
applyLambdaEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
isect_memberFormation,
promote_hyp,
tokenEquality,
equalityElimination,
instantiate,
cumulativity,
atomEquality,
pointwiseFunctionality,
baseApply,
closedConclusion,
baseClosed,
callbyvalueReduce,
productEquality,
imageMemberEquality,
imageElimination,
addLevel,
levelHypothesis
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p,q:polyform(n)]. (add-polynom(p;q) \mmember{} polyform(n))
Date html generated:
2017_10_01-AM-08_32_46
Last ObjectModification:
2017_07_12-PM-00_01_30
Theory : integer!polynomial!trees
Home
Index