Nuprl Lemma : mul-minus-2
∀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 :
all: ∀x:A. B[x],
has-value: (a)↓,
member: t ∈ T,
and: P ∧ Q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
top: Top,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
value-type-has-value,
int-value-type,
has-value_wf_base,
is-exception_wf,
istype-top,
subtype_base_sq,
int_subtype_base,
minus-one-mul,
mul-swap,
istype-void,
minus-one-mul-top,
int-mul-exception
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
sqequalRule,
thin,
sqequalSqle,
divergentSqle,
callbyvalueMultiply,
sqequalHypSubstitution,
hypothesis,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
productElimination,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
introduction,
extract_by_obid,
isectElimination,
intEquality,
independent_isectElimination,
Error :equalityIstype,
dependent_functionElimination,
independent_functionElimination,
callbyvalueMinus,
multiplyExceptionCases,
axiomSqleEquality,
minusExceptionCases,
exceptionSqequal,
sqleReflexivity,
because_Cache,
instantiate,
cumulativity,
Error :isect_memberEquality_alt,
voidElimination,
multiplyEquality,
minusEquality
Latex:
\mforall{}x,y:Top. (x * (-y) \msim{} -(x * y))
Date html generated:
2019_06_20-AM-11_22_16
Last ObjectModification:
2019_05_21-PM-10_55_32
Theory : arithmetic
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