Nuprl Lemma : add-mul-special
∀[x:ℤ]. ∀[y:Top]. (x + (y * x) ~ (1 + y) * x)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
top_wf,
mul-distributes-right,
one-mul
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
intEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[x:\mBbbZ{}]. \mforall{}[y:Top]. (x + (y * x) \msim{} (1 + y) * x)
Date html generated:
2016_05_13-PM-03_29_29
Last ObjectModification:
2015_12_26-AM-09_47_48
Theory : arithmetic
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