Nuprl Lemma : poly_int_val_cons_cons-sq
∀n:ℕ. ∀p:polyform(n) List. ∀l:{l:ℤ List| ||l|| = n ∈ ℤ} . ∀a:ℤ. ∀u:polyform(n).
([a / l]@[u / p] ~ (l@u * a^||p||) + [a / l]@p)
Proof
Definitions occuring in Statement :
poly-int-val: l@p,
polyform: polyform(n),
exp: i^n,
length: ||as||,
cons: [a / b],
list: T List,
nat: ℕ,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
multiply: n * m,
add: n + m,
int: ℤ,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
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,
poly_int_val_cons_cons,
polyform_wf,
istype-int,
list_wf,
length_wf_nat,
set_subtype_base,
le_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
Error :universeIsType,
Error :setIsType,
Error :equalityIsType4,
applyEquality,
sqequalRule,
Error :lambdaEquality_alt,
natural_numberEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}p:polyform(n) List. \mforall{}l:\{l:\mBbbZ{} List| ||l|| = n\} . \mforall{}a:\mBbbZ{}. \mforall{}u:polyform(n).
([a / l]@[u / p] \msim{} (l@u * a\^{}||p||) + [a / l]@p)
Date html generated:
2019_06_20-PM-01_52_06
Last ObjectModification:
2018_10_04-PM-00_19_30
Theory : integer!polynomials
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