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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