Nuprl Lemma : int-rdiv-int-rmul
∀[k:ℤ-o]. ∀[a:ℝ]. (k * (a)/k = a)
Proof
Definitions occuring in Statement :
int-rdiv: (a)/k1,
int-rmul: k1 * a,
req: x = y,
real: ℝ,
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_nzero: ℤ-o,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bdd-diff: bdd-diff(f;g),
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
real: ℝ,
prop: ℙ,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
int-rdiv: (a)/k1,
int-rmul: k1 * a,
has-value: (a)↓,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
less_than: a < b,
true: True,
nat_plus: ℕ+,
nequal: a ≠ b ∈ T ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
regular-int-seq: k-regular-seq(f),
rev_uimplies: rev_uimplies(P;Q),
ge: i ≥ j ,
int_lower: {...i},
absval: |i|,
subtract: n - m
Latex:
\mforall{}[k:\mBbbZ{}\msupminus{}\msupzero{}]. \mforall{}[a:\mBbbR{}]. (k * (a)/k = a)
Date html generated:
2020_05_20-AM-10_55_06
Last ObjectModification:
2019_12_26-PM-10_01_01
Theory : reals
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