Nuprl Lemma : add-polynom-int-val-sq
∀[n:ℕ]. ∀[l:{l:ℤ List| ||l|| = n ∈ ℤ} ]. ∀[p,q:polyform(n)]. ∀[rmz:𝔹]. (l@add-polynom(n;rmz;p;q) ~ l@p + l@q)
Proof
Definitions occuring in Statement :
add-polynom: add-polynom(n;rmz;p;q),
poly-int-val: l@p,
polyform: polyform(n),
length: ||as||,
list: T List,
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
add: n + m,
int: ℤ,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
add-polynom-int-val,
bool_wf,
polyform_wf,
list_wf,
istype-int,
length_wf_nat,
set_subtype_base,
le_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomSqEquality,
Error :universeIsType,
sqequalRule,
Error :isect_memberEquality_alt,
because_Cache,
Error :inhabitedIsType,
Error :setIsType,
Error :equalityIsType4,
applyEquality,
Error :lambdaEquality_alt,
natural_numberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[l:\{l:\mBbbZ{} List| ||l|| = n\} ]. \mforall{}[p,q:polyform(n)]. \mforall{}[rmz:\mBbbB{}].
(l@add-polynom(n;rmz;p;q) \msim{} l@p + l@q)
Date html generated:
2019_06_20-PM-01_52_21
Last ObjectModification:
2018_10_04-PM-00_15_06
Theory : integer!polynomials
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