### Nuprl Lemma : flip-conjugation1

`∀[n:ℕ]. ∀[k:ℕn - 1]. ∀[j:ℕk].  ((j, k + 1) = ((k, k + 1) o ((j, k) o (k, k + 1))) ∈ (ℕn ⟶ ℕn))`

Proof

Definitions occuring in Statement :  flip: `(i, j)` compose: `f o g` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` function: `x:A ⟶ B[x]` subtract: `n - m` add: `n + m` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` int_seg: `{i..j-}` lelt: `i ≤ j < k` and: `P ∧ Q` guard: `{T}` nat: `ℕ` ge: `i ≥ j ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` prop: `ℙ`
Lemmas referenced :  nat_wf int_seg_wf subtract_wf lelt_wf int_formula_prop_wf int_term_value_constant_lemma int_term_value_subtract_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermConstant_wf itermSubtract_wf itermVar_wf intformless_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__lt nat_properties int_seg_properties flip-conjugation
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality setElimination rename dependent_set_memberEquality because_Cache productElimination independent_pairFormation hypothesis dependent_functionElimination unionElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality sqequalRule computeAll axiomEquality

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[k:\mBbbN{}n  -  1].  \mforall{}[j:\mBbbN{}k].    ((j,  k  +  1)  =  ((k,  k  +  1)  o  ((j,  k)  o  (k,  k  +  1))))

Date html generated: 2016_05_14-PM-02_13_29
Last ObjectModification: 2016_01_15-AM-07_57_05

Theory : list_1

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