Nuprl Lemma : polynom-subtype-list
∀[n:ℕ+]. (polynom(n) ⊆r (polynom(n - 1) List))
Proof
Definitions occuring in Statement :
polynom: polynom(n),
list: T List,
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n
Definitions unfolded in proof :
polyform: polyform(n),
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,
or: P ∨ Q,
decidable: Dec(P),
nat: ℕ,
prop: ℙ,
and: P ∧ Q,
top: Top,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
nat_plus: ℕ+,
polynom: polynom(n),
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
polynom_subtype_polyform,
polyform_wf,
subtype_rel_list,
equal_wf,
assert_of_bnot,
eqff_to_assert,
iff_weakening_uiff,
iff_transitivity,
assert_of_eq_int,
eqtt_to_assert,
uiff_transitivity,
nat_plus_subtype_nat,
polyform-lead-nonzero_wf,
le_wf,
int_term_value_subtract_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformle_wf,
intformnot_wf,
decidable__le,
subtract_wf,
polynom_wf,
list_wf,
not_wf,
bnot_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_plus_properties,
assert_wf,
equal-wf-T-base,
bool_wf,
eq_int_wf,
nat_plus_wf
Rules used in proof :
impliesFunctionality,
productElimination,
independent_functionElimination,
equalityElimination,
lambdaFormation,
applyEquality,
unionElimination,
dependent_set_memberEquality,
setEquality,
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
intEquality,
because_Cache,
baseClosed,
equalitySymmetry,
equalityTransitivity,
natural_numberEquality,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesis,
axiomEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. (polynom(n) \msubseteq{}r (polynom(n - 1) List))
Date html generated:
2017_04_20-AM-07_08_16
Last ObjectModification:
2017_04_19-AM-11_31_03
Theory : list_1
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