Nuprl Lemma : add_mono_wrt_eq
∀[a,b,n:ℤ]. uiff(a = b ∈ ℤ;(a + n) = (b + n) ∈ ℤ)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
add: n + m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
equal_wf,
add_cancel_in_eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
addEquality,
hypothesis,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
sqequalRule,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination
Latex:
\mforall{}[a,b,n:\mBbbZ{}]. uiff(a = b;(a + n) = (b + n))
Date html generated:
2016_05_13-PM-03_39_50
Last ObjectModification:
2015_12_26-AM-09_40_46
Theory : arithmetic
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