### Nuprl Lemma : rmaximum-constant

`∀[n,m:ℤ].  ∀[x:{n..m + 1-} ⟶ ℝ]. ∀[r:ℝ].  rmaximum(n;m;i.x[i]) = r supposing ∀i:{n..m + 1-}. (x[i] = r) supposing n ≤ m`

Proof

Definitions occuring in Statement :  rmaximum: `rmaximum(n;m;k.x[k])` req: `x = y` real: `ℝ` int_seg: `{i..j-}` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` so_apply: `x[s]` le: `A ≤ B` all: `∀x:A. B[x]` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` rmaximum: `rmaximum(n;m;k.x[k])` nat: `ℕ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` not: `¬A` implies: `P `` Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` and: `P ∧ Q` prop: `ℙ` guard: `{T}` ge: `i ≥ j ` sq_type: `SQType(T)` le: `A ≤ B` less_than': `less_than'(a;b)` so_apply: `x[s]` int_seg: `{i..j-}` lelt: `i ≤ j < k` so_lambda: `λ2x.t[x]` top: `Top` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` subtype_rel: `A ⊆r B` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` cand: `A c∧ B` less_than: `a < b` squash: `↓T` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` subtract: `n - m` true: `True` rev_uimplies: `rev_uimplies(P;Q)`

Latex:
\mforall{}[n,m:\mBbbZ{}].
\mforall{}[x:\{n..m  +  1\msupminus{}\}  {}\mrightarrow{}  \mBbbR{}].  \mforall{}[r:\mBbbR{}].    rmaximum(n;m;i.x[i])  =  r  supposing  \mforall{}i:\{n..m  +  1\msupminus{}\}.  (x[i]  =  r)
supposing  n  \mleq{}  m

Date html generated: 2020_05_20-AM-11_14_41
Last ObjectModification: 2020_01_06-PM-00_25_05

Theory : reals

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