Nuprl Lemma : minus-one-mul
∀[x:ℤ]. (-x ~ (-1) * x)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
multiply: n * m,
minus: -n,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
top: Top,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T}
Lemmas referenced :
add-inverse-unique,
mul-distributes-right,
one-mul,
zero-mul,
subtype_base_sq,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
intEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
multiplyEquality,
minusEquality,
natural_numberEquality,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
instantiate,
cumulativity,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x:\mBbbZ{}]. (-x \msim{} (-1) * x)
Date html generated:
2016_05_13-PM-03_29_20
Last ObjectModification:
2015_12_26-AM-09_47_42
Theory : arithmetic
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