### Nuprl Lemma : flip_inverse

`∀[k:ℤ]. ∀[x,y:ℕk].  (((y, x) o (y, x)) = (λx.x) ∈ (ℕk ⟶ ℕk))`

Proof

Definitions occuring in Statement :  flip: `(i, j)` compose: `f o g` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` flip: `(i, j)` compose: `f o g` int_seg: `{i..j-}` implies: `P `` Q` guard: `{T}` lelt: `i ≤ j < k` and: `P ∧ Q` 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` not: `¬A` top: `Top` prop: `ℙ` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` nequal: `a ≠ b ∈ T ` squash: `↓T` true: `True` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  int_seg_wf eq_int_wf ifthenelse_wf bool_wf equal-wf-T-base assert_wf equal_wf int_seg_properties decidable__equal_int satisfiable-full-omega-tt intformand_wf intformnot_wf intformeq_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_formula_prop_wf decidable__le intformle_wf itermConstant_wf int_formula_prop_le_lemma int_term_value_constant_lemma decidable__lt intformless_wf int_formula_prop_less_lemma bnot_wf not_wf lelt_wf eqtt_to_assert assert_of_eq_int eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int and_wf eq_int_eq_true btrue_wf iff_weakening_equal uiff_transitivity iff_transitivity iff_weakening_uiff assert_of_bnot
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut functionExtensionality sqequalRule because_Cache hypothesis extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality hypothesisEquality isect_memberEquality axiomEquality intEquality setElimination rename equalityTransitivity equalitySymmetry baseClosed independent_functionElimination lambdaFormation productElimination dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality voidElimination voidEquality independent_pairFormation computeAll dependent_set_memberEquality equalityElimination promote_hyp instantiate cumulativity applyLambdaEquality applyEquality imageElimination imageMemberEquality impliesFunctionality

Latex:
\mforall{}[k:\mBbbZ{}].  \mforall{}[x,y:\mBbbN{}k].    (((y,  x)  o  (y,  x))  =  (\mlambda{}x.x))

Date html generated: 2017_04_17-AM-08_06_33
Last ObjectModification: 2017_02_27-PM-04_35_40

Theory : list_1

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