Nuprl Lemma : add_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],
add: n + m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
addEquality,
hypothesis,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
because_Cache,
isect_memberFormation,
introduction,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[i1,i2,j1,j2:\mBbbZ{}]. ((i1 + i2) = (j1 + j2)) supposing ((i2 = j2) and (i1 = j1))
Date html generated:
2016_05_13-PM-03_30_53
Last ObjectModification:
2015_12_26-AM-09_46_25
Theory : arithmetic
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