Nuprl Lemma : minus-one-mul-top
∀[x:Top]. (-x ~ (-1) * x)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
multiply: n * m,
minus: -n,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
false: False
Lemmas referenced :
top_wf,
exception-not-value,
is-exception_wf,
has-value_wf_base,
minus-one-mul
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
sqequalSqle,
divergentSqle,
callbyvalueMinus,
sqequalHypSubstitution,
hypothesis,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
lemma_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
sqleReflexivity,
minusExceptionCases,
axiomSqleEquality,
exceptionSqequal,
callbyvalueMultiply,
productElimination,
multiplyExceptionCases,
independent_isectElimination,
independent_functionElimination,
voidElimination,
sqequalAxiom
Latex:
\mforall{}[x:Top]. (-x \msim{} (-1) * x)
Date html generated:
2016_05_13-PM-03_29_22
Last ObjectModification:
2016_01_14-PM-06_41_40
Theory : arithmetic
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