Nuprl Lemma : select-int-vec-mul
∀[x:ℤ]. ∀[as:ℤ List]. ∀[i:ℕ||as||]. (x * as[i] ~ x * as[i])
Proof
Definitions occuring in Statement :
int-vec-mul: a * as,
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
multiply: n * m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int-vec-mul: a * as,
top: Top,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T}
Lemmas referenced :
list_wf,
length_wf,
int_seg_wf,
sq_stable__le,
select_wf,
top_wf,
subtype_rel_list,
select-map,
int_subtype_base,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
applyEquality,
lambdaEquality,
multiplyEquality,
intEquality,
setElimination,
rename,
natural_numberEquality,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
sqequalAxiom
Latex:
\mforall{}[x:\mBbbZ{}]. \mforall{}[as:\mBbbZ{} List]. \mforall{}[i:\mBbbN{}||as||]. (x * as[i] \msim{} x * as[i])
Date html generated:
2016_05_14-AM-06_56_43
Last ObjectModification:
2016_01_14-PM-08_44_35
Theory : omega
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