Nuprl Lemma : two-mul
∀[x:Top]. (x + x ~ 2 * x)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
multiply: n * m,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
has-value: (a)↓,
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
false: False
Lemmas referenced :
top_wf,
int-value-type,
value-type-has-value,
exception-not-value,
is-exception_wf,
has-value_wf_base,
one-mul,
mul-distributes-right
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
hypothesis,
sqequalAxiom,
intEquality,
sqequalRule,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalSqle,
sqleRule,
divergentSqle,
callbyvalueAdd,
baseApply,
closedConclusion,
baseClosed,
productElimination,
equalityTransitivity,
equalitySymmetry,
sqleReflexivity,
addExceptionCases,
axiomSqleEquality,
exceptionSqequal,
callbyvalueMultiply,
multiplyExceptionCases,
independent_isectElimination,
natural_numberEquality,
independent_functionElimination
Latex:
\mforall{}[x:Top]. (x + x \msim{} 2 * x)
Date html generated:
2016_05_13-PM-03_29_27
Last ObjectModification:
2016_01_14-PM-06_41_47
Theory : arithmetic
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