Nuprl Lemma : polynom_subtype_polyform
∀[n:ℕ]. (polynom(n) ⊆r polyform(n))
Proof
Definitions occuring in Statement :
polynom: polynom(n),
polyform: polyform(n),
nat: ℕ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
so_apply: x[s],
squash: ↓T,
so_lambda: λ2x.t[x],
polyform-lead-nonzero: polyform-lead-nonzero(n;p),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
bfalse: ff,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
less_than: a < b,
polyform: polyform(n),
polynom: polynom(n),
less_than': less_than'(a;b),
le: A ≤ B,
or: P ∨ Q,
decidable: Dec(P),
lelt: i ≤ j < k,
int_seg: {i..j-},
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
and: P ∧ Q,
top: Top,
not: ¬A,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
subtype_rel_list,
hd_wf,
poly-zero_wf,
length_wf,
polyform_wf,
polynom_wf,
list_wf,
subtype_rel_set,
subtype_rel_self,
equal_wf,
assert_of_bnot,
eqff_to_assert,
iff_weakening_uiff,
iff_transitivity,
assert_of_eq_int,
eqtt_to_assert,
uiff_transitivity,
not_wf,
bnot_wf,
assert_wf,
equal-wf-T-base,
bool_wf,
eq_int_wf,
nat_wf,
int_term_value_add_lemma,
itermAdd_wf,
lelt_wf,
decidable__lt,
le_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
false_wf,
int_seg_subtype,
decidable__equal_int,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
int_seg_properties,
int_seg_wf,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties
Rules used in proof :
imageElimination,
functionEquality,
impliesFunctionality,
equalityElimination,
baseClosed,
addEquality,
dependent_set_memberEquality,
hypothesis_subsumption,
applyLambdaEquality,
equalitySymmetry,
equalityTransitivity,
applyEquality,
unionElimination,
productElimination,
because_Cache,
axiomEquality,
independent_functionElimination,
computeAll,
independent_pairFormation,
sqequalRule,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
natural_numberEquality,
intWeakElimination,
rename,
setElimination,
hypothesis,
hypothesisEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaFormation,
thin,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]. (polynom(n) \msubseteq{}r polyform(n))
Date html generated:
2017_04_17-AM-09_03_41
Last ObjectModification:
2017_04_13-PM-01_09_07
Theory : list_1
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