Nuprl Lemma : minus-add
∀[x,y:Top]. (-(x + y) ~ (-x) + (-y))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
minus: -n,
sqequal: s ~ t
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
top: Top,
guard: {T},
sq_type: SQType(T),
and: P ∧ Q,
prop: ℙ,
uimplies: b supposing a,
has-value: (a)↓
Lemmas referenced :
add-inverse-unique,
minus-one-mul,
add-associates,
istype-void,
istype-int,
minus-one-mul-top,
add-swap,
add-mul-special,
zero-mul,
zero-add,
top_wf,
is-exception_wf,
has-value_wf_base,
int_subtype_base,
subtype_base_sq,
equal_wf,
int-value-type,
value-type-has-value,
int-add-exception
Rules used in proof :
cut,
intEquality,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
minusEquality,
hypothesisEquality,
addEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
equalitySymmetry,
sqequalRule,
applyEquality,
Error :lambdaEquality_alt,
Error :isect_memberEquality_alt,
voidElimination,
because_Cache,
natural_numberEquality,
multiplyEquality,
isect_memberEquality,
axiomSqEquality,
exceptionSqequal,
addExceptionCases,
axiomSqleEquality,
minusExceptionCases,
sqleReflexivity,
cumulativity,
instantiate,
productElimination,
callbyvalueAdd,
dependent_functionElimination,
independent_isectElimination,
equalityTransitivity,
baseClosed,
closedConclusion,
baseApply,
callbyvalueMinus,
divergentSqle,
sqleRule,
sqequalSqle,
isect_memberFormation,
voidEquality
Latex:
\mforall{}[x,y:Top]. (-(x + y) \msim{} (-x) + (-y))
Date html generated:
2019_06_20-AM-11_22_21
Last ObjectModification:
2018_10_16-PM-04_55_33
Theory : arithmetic
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