### Nuprl Lemma : sq_stable__is-partition-choice

`∀[p:ℝ List]. ∀[x:ℕ||p|| - 1 ⟶ ℝ].  SqStable(is-partition-choice(p;x))`

Proof

Definitions occuring in Statement :  is-partition-choice: `is-partition-choice(p;x)` real: `ℝ` length: `||as||` list: `T List` int_seg: `{i..j-}` sq_stable: `SqStable(P)` uall: `∀[x:A]. B[x]` function: `x:A ⟶ B[x]` subtract: `n - m` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` is-partition-choice: `is-partition-choice(p;x)` member: `t ∈ T` so_lambda: `λ2x.t[x]` int_seg: `{i..j-}` uimplies: `b supposing a` guard: `{T}` lelt: `i ≤ j < k` and: `P ∧ Q` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` prop: `ℙ` less_than: `a < b` squash: `↓T` uiff: `uiff(P;Q)` so_apply: `x[s]` i-member: `r ∈ I` rccint: `[l, u]` sq_stable: `SqStable(P)` rleq: `x ≤ y` rnonneg: `rnonneg(x)` le: `A ≤ B` subtype_rel: `A ⊆r B`
Lemmas referenced :  list_wf squash_wf nat_plus_wf rsub_wf less_than'_wf sq_stable__rleq rleq_wf sq_stable__and int_term_value_add_lemma itermAdd_wf false_wf int_term_value_subtract_lemma int_formula_prop_less_lemma itermSubtract_wf intformless_wf subtract-is-int-iff decidable__lt int_formula_prop_wf int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le int_seg_properties select_wf rccint_wf i-member_wf real_wf length_wf subtract_wf int_seg_wf sq_stable__all
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality hypothesis hypothesisEquality sqequalRule lambdaEquality setElimination rename independent_isectElimination productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll because_Cache pointwiseFunctionality equalityTransitivity equalitySymmetry promote_hyp imageElimination baseApply closedConclusion baseClosed addEquality applyEquality independent_functionElimination lambdaFormation introduction independent_pairEquality minusEquality axiomEquality functionEquality

Latex:
\mforall{}[p:\mBbbR{}  List].  \mforall{}[x:\mBbbN{}||p||  -  1  {}\mrightarrow{}  \mBbbR{}].    SqStable(is-partition-choice(p;x))

Date html generated: 2016_05_18-AM-09_03_24
Last ObjectModification: 2016_01_17-AM-02_32_59

Theory : reals

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