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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