Nuprl Lemma : nat-mul-absval
∀[n:ℕ]. ∀[x:ℤ]. ((n * |x|) = |n * x| ∈ ℤ)
Proof
Definitions occuring in Statement :
absval: |i|,
nat: ℕ,
uall: ∀[x:A]. B[x],
multiply: n * m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
uimplies: b supposing a,
true: True,
subtype_rel: A ⊆r B,
nat: ℕ,
squash: ↓T,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
istype-int,
absval_pos,
iff_weakening_equal,
absval_mul,
absval_wf,
equal_wf
Rules used in proof :
isectIsTypeImplies,
axiomEquality,
isect_memberEquality_alt,
independent_functionElimination,
productElimination,
independent_isectElimination,
baseClosed,
imageMemberEquality,
natural_numberEquality,
sqequalRule,
equalitySymmetry,
equalityTransitivity,
inhabitedIsType,
hypothesisEquality,
rename,
setElimination,
multiplyEquality,
intEquality,
hypothesis,
because_Cache,
isectElimination,
extract_by_obid,
imageElimination,
sqequalHypSubstitution,
lambdaEquality_alt,
thin,
applyEquality,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x:\mBbbZ{}]. ((n * |x|) = |n * x|)
Date html generated:
2019_10_15-AM-10_19_42
Last ObjectModification:
2019_10_10-PM-00_20_17
Theory : arithmetic
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