### 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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