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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