Nuprl Lemma : int-rdiv_wf
∀[k:ℤ-o]. ∀[a:ℝ]. ((a)/k ∈ ℝ)
Proof
Definitions occuring in Statement :
int-rdiv: (a)/k1,
real: ℝ,
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real: ℝ,
int-rdiv: (a)/k1,
has-value: (a)↓,
uimplies: b supposing a,
int_nzero: ℤ-o,
so_lambda: λ2x.t[x],
so_apply: x[s],
regular-int-seq: k-regular-seq(f),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
nequal: a ≠ b ∈ T ,
nat_plus: ℕ+,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
less_than: a < b,
squash: ↓T,
true: True,
guard: {T},
le: A ≤ B,
less_than': less_than'(a;b),
sq_type: SQType(T),
subtract: n - m,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q),
ge: i ≥ j ,
sq_stable: SqStable(P),
int_upper: {i...}
Latex:
\mforall{}[k:\mBbbZ{}\msupminus{}\msupzero{}]. \mforall{}[a:\mBbbR{}]. ((a)/k \mmember{} \mBbbR{})
Date html generated:
2020_05_20-AM-10_54_56
Last ObjectModification:
2019_12_26-PM-09_05_44
Theory : reals
Home
Index