Nuprl Lemma : mul-minus
∀x,y:Top.  ((-x) * (-y) ~ x * y)
Proof
Definitions occuring in Statement : 
top: Top
, 
all: ∀x:A. B[x]
, 
multiply: n * m
, 
minus: -n
, 
sqequal: s ~ t
Definitions unfolded in proof : 
top: Top
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
has-value: (a)↓
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
squash: ↓T
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
true: True
, 
uimplies: b supposing a
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
false: False
Lemmas referenced : 
istype-void, 
has-value_wf_base, 
squash_wf, 
true_wf, 
istype-base, 
int_subtype_base, 
subtype_rel_self, 
iff_weakening_equal, 
add-zero, 
sqle_wf_base, 
add-comm, 
zero-add-sqle, 
exception-not-value, 
value-type-has-value, 
int-value-type, 
is-exception_wf, 
istype-top, 
mul-minus-1, 
mul-minus-2, 
minus-minus-sq
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberEquality_alt, 
voidElimination, 
cut, 
introduction, 
extract_by_obid, 
hypothesis, 
Error :lambdaFormation_alt, 
sqequalRule, 
thin, 
sqequalSqle, 
divergentSqle, 
callbyvalueAdd, 
sqequalHypSubstitution, 
baseApply, 
closedConclusion, 
baseClosed, 
hypothesisEquality, 
productElimination, 
equalityTransitivity, 
equalitySymmetry, 
Error :inhabitedIsType, 
applyEquality, 
Error :lambdaEquality_alt, 
imageElimination, 
isectElimination, 
Error :universeIsType, 
natural_numberEquality, 
imageMemberEquality, 
instantiate, 
universeEquality, 
independent_isectElimination, 
independent_functionElimination, 
Error :equalityIstype, 
dependent_functionElimination, 
callbyvalueMultiply, 
because_Cache, 
addExceptionCases, 
axiomSqleEquality, 
intEquality, 
multiplyExceptionCases, 
exceptionSqequal, 
sqleReflexivity, 
multiplyEquality
Latex:
\mforall{}x,y:Top.    ((-x)  *  (-y)  \msim{}  x  *  y)
Date html generated:
2019_06_20-AM-11_22_19
Last ObjectModification:
2019_05_21-PM-11_03_07
Theory : arithmetic
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