Nuprl Lemma : polyform-value-type
∀[n:ℕ]. value-type(polyform(n))
Proof
Definitions occuring in Statement :
polyform: polyform(n),
nat: ℕ,
value-type: value-type(T),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
value-type: value-type(T),
has-value: (a)↓,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
polyform: polyform(n),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
less_than: a < b
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
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,
equal-wf-base,
polyform_wf,
less_than_transitivity1,
less_than_irreflexivity,
base_wf,
int_seg_wf,
int_seg_properties,
int_seg_subtype_nat,
false_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
decidable__equal_int,
int_seg_subtype,
intformeq_wf,
int_formula_prop_eq_lemma,
le_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
int-value-type,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
list-value-type,
decidable__lt,
lelt_wf,
itermAdd_wf,
int_term_value_add_lemma,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomSqleEquality,
applyEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
productElimination,
unionElimination,
applyLambdaEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
equalityElimination,
promote_hyp,
instantiate,
cumulativity,
addEquality
Latex:
\mforall{}[n:\mBbbN{}]. value-type(polyform(n))
Date html generated:
2017_09_29-PM-05_59_45
Last ObjectModification:
2017_05_02-PM-03_09_26
Theory : integer!polynomials
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