Nuprl Lemma : rem_nrel_wf
∀[a:ℕ]. ∀[n:ℕ+]. ∀[r:ℕ].  (Rem(a;n;r) ∈ ℙ)
Proof
Definitions occuring in Statement : 
rem_nrel: Rem(a;n;r)
, 
nat_plus: ℕ+
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
rem_nrel: Rem(a;n;r)
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
and: P ∧ Q
, 
nat: ℕ
, 
nat_plus: ℕ+
, 
so_apply: x[s]
Lemmas referenced : 
exists_wf, 
nat_wf, 
div_nrel_wf, 
equal_wf, 
nat_plus_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
lambdaEquality, 
productEquality, 
hypothesisEquality, 
intEquality, 
addEquality, 
multiplyEquality, 
setElimination, 
rename, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
Error :inhabitedIsType, 
isect_memberEquality, 
Error :universeIsType, 
because_Cache
Latex:
\mforall{}[a:\mBbbN{}].  \mforall{}[n:\mBbbN{}\msupplus{}].  \mforall{}[r:\mBbbN{}].    (Rem(a;n;r)  \mmember{}  \mBbbP{})
Date html generated:
2019_06_20-PM-01_14_38
Last ObjectModification:
2018_09_26-PM-02_32_22
Theory : int_2
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