Nuprl Lemma : absval_squared
∀[x:ℤ]. ((|x| * |x|) = (x * x) ∈ ℤ)
Proof
Definitions occuring in Statement :
absval: |i|,
uall: ∀[x:A]. B[x],
multiply: n * m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
absval_mul,
absval_square,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
hypothesis,
intEquality,
because_Cache,
hypothesisEquality,
multiplyEquality,
natural_numberEquality,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
equalitySymmetry,
equalityTransitivity,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[x:\mBbbZ{}]. ((|x| * |x|) = (x * x))
Date html generated:
2017_04_14-AM-09_15_38
Last ObjectModification:
2017_02_27-PM-03_53_05
Theory : int_2
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