Nuprl Lemma : mul_preserves_eq
∀[a,b,n:ℤ]. (n * a) = (n * b) ∈ ℤ supposing a = b ∈ ℤ
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
multiply: n * m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
multiplyEquality,
hypothesisEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b,n:\mBbbZ{}]. (n * a) = (n * b) supposing a = b
Date html generated:
2016_05_13-PM-03_34_34
Last ObjectModification:
2015_12_26-AM-09_43_32
Theory : arithmetic
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