Nuprl Lemma : mul_functionality_wrt_eq
∀[i1,i2,j1,j2:ℤ]. ((i1 * i2) = (j1 * j2) ∈ ℤ) supposing ((i2 = j2 ∈ ℤ) and (i1 = j1 ∈ 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,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[i1,i2,j1,j2:\mBbbZ{}]. ((i1 * i2) = (j1 * j2)) supposing ((i2 = j2) and (i1 = j1))
Date html generated:
2016_05_14-AM-07_20_35
Last ObjectModification:
2015_12_26-PM-01_32_17
Theory : int_2
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