Nuprl Lemma : int-vec-mul-mul
∀[a,b:ℤ]. ∀[as:ℤ List]. (a * b * as ~ a * b * as)
Proof
Definitions occuring in Statement :
int-vec-mul: a * as,
list: T List,
uall: ∀[x:A]. B[x],
multiply: n * m,
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,
compose: f o g,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
prop: ℙ
Lemmas referenced :
true_wf,
squash_wf,
map_wf,
mul-associates,
map-map,
int_subtype_base,
list_subtype_base,
list_wf,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
because_Cache,
hypothesisEquality,
functionExtensionality,
applyEquality,
lambdaEquality,
multiplyEquality,
natural_numberEquality,
imageElimination,
functionEquality,
universeEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[a,b:\mBbbZ{}]. \mforall{}[as:\mBbbZ{} List]. (a * b * as \msim{} a * b * as)
Date html generated:
2016_05_14-AM-06_56_29
Last ObjectModification:
2016_01_14-PM-08_44_32
Theory : omega
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