Nuprl Lemma : div_base_case
∀[a:ℕ]. ∀[n:ℕ+]. (a ÷ n) = 0 ∈ ℤ supposing a < n
Proof
Definitions occuring in Statement :
nat_plus: ℕ+,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
divide: n ÷ m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
nat: ℕ,
nat_plus: ℕ+
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
quotient-is-zero,
nat_plus_subtype_nat,
subtype_rel_self,
iff_weakening_equal,
less_than_wf,
nat_plus_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
intEquality,
sqequalRule,
independent_isectElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
because_Cache,
productElimination,
independent_functionElimination,
Error :universeIsType,
setElimination,
rename,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[a:\mBbbN{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. (a \mdiv{} n) = 0 supposing a < n
Date html generated:
2019_06_20-PM-01_14_44
Last ObjectModification:
2018_09_26-PM-02_35_51
Theory : int_2
Home
Index