Nuprl Lemma : remainder_wf
∀[a:ℕ]. ∀[n:ℕ+]. (a rem n ∈ ℕ)
Proof
Definitions occuring in Statement :
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
remainder: n rem m
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
subtype_rel: A ⊆r B,
and: P ∧ Q
Lemmas referenced :
remainder_wfa,
nat_plus_inc_int_nzero,
rem_bounds_1,
istype-le,
nat_plus_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :dependent_set_memberEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
productElimination,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType
Latex:
\mforall{}[a:\mBbbN{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. (a rem n \mmember{} \mBbbN{})
Date html generated:
2019_06_20-PM-02_12_29
Last ObjectModification:
2019_06_20-PM-02_08_52
Theory : int_2
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