Nuprl Lemma : int-rem-exception
∀[x:ℤ]. ∀[u,v:Top]. (x rem exception(u; v) ~ exception(u; v))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
remainder: n rem m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
istype-top,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
exceptionRemainder,
hypothesisEquality,
hypothesis,
axiomSqEquality,
Error :inhabitedIsType,
sqequalRule,
sqequalHypSubstitution,
Error :isect_memberEquality_alt,
isectElimination,
thin,
extract_by_obid
Latex:
\mforall{}[x:\mBbbZ{}]. \mforall{}[u,v:Top]. (x rem exception(u; v) \msim{} exception(u; v))
Date html generated:
2019_06_20-AM-11_22_00
Last ObjectModification:
2018_10_12-PM-03_56_40
Theory : arithmetic
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