Nuprl Lemma : ppcc-test
∀[a,b,c:ℤ]. ((a + c) = (c + c) ∈ ℤ) supposing (((b + c) = (c + c) ∈ ℤ) and (a = b ∈ 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 :
prop: ℙ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q
Lemmas referenced :
equal_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
isect_memberEquality,
sqequalRule,
introduction,
isect_memberFormation,
because_Cache,
hypothesis,
hypothesisEquality,
addEquality,
intEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
dependent_set_memberEquality_alt,
independent_pairFormation,
productIsType,
equalityIstype,
inhabitedIsType,
applyLambdaEquality,
setElimination,
rename,
productElimination
Latex:
\mforall{}[a,b,c:\mBbbZ{}]. ((a + c) = (c + c)) supposing (((b + c) = (c + c)) and (a = b))
Date html generated:
2020_05_20-AM-08_05_04
Last ObjectModification:
2020_01_07-PM-01_12_37
Theory : general
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