Nuprl Lemma : compose-polynom_wf
∀[n:ℕ]. ∀[p,q:polynom(n)]. (compose-polynom(n;p;q) ∈ polynom(n))
Proof
Definitions occuring in Statement :
compose-polynom: compose-polynom(n;p;q),
polynom: polynom(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
compose-polynom: compose-polynom(n;p;q),
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_apply: x[s1;s2],
polynom: polynom(n),
polyform-lead-nonzero: polyform-lead-nonzero(n;p),
less_than: a < b,
squash: ↓T
Lemmas referenced :
eq_int_wf,
uiff_transitivity,
equal-wf-base,
bool_wf,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
istype-assert,
istype-void,
list_accum_wf,
polynom_wf,
subtract_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
istype-le,
polyconst_wf2,
poly-zero_wf,
polynom_subtype_polyform,
mul-polynom_wf2,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
add-polynom_wf,
istype-nat,
bool_cases,
subtype_rel-equal,
nat_wf,
base_wf,
cons_wf,
nil_wf,
length_of_cons_lemma,
length_of_nil_lemma,
reduce_hd_cons_lemma,
istype-less_than,
length_wf,
intformless_wf,
int_formula_prop_less_lemma,
hd_wf,
polyform_wf,
subtype_rel_list
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
intEquality,
Error :lambdaEquality_alt,
independent_isectElimination,
because_Cache,
independent_functionElimination,
productElimination,
independent_pairFormation,
Error :equalityIstype,
sqequalBase,
equalitySymmetry,
Error :functionIsType,
voidElimination,
Error :dependent_set_memberEquality_alt,
dependent_functionElimination,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
Error :universeIsType,
equalityTransitivity,
promote_hyp,
instantiate,
cumulativity,
axiomEquality,
Error :isectIsTypeImplies,
imageElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p,q:polynom(n)]. (compose-polynom(n;p;q) \mmember{} polynom(n))
Date html generated:
2019_06_20-PM-01_54_05
Last ObjectModification:
2019_01_20-AM-11_55_27
Theory : integer!polynomials
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