Nuprl Lemma : tswap_eval_2

n:ℕ. ∀i,j,k:ℕn.  ((k j ∈ ℕn)  ((swap{n}(i;j) k) i ∈ ℕn))


Proof




Definitions occuring in Statement :  tswap: swap{n}(i;j) int_seg: {i..j-} nat: all: x:A. B[x] implies:  Q apply: a natural_number: $n equal: t ∈ T
Definitions unfolded in proof :  tswap: swap{n}(i;j) all: x:A. B[x] implies:  Q int_seg: {i..j-} lelt: i ≤ j < k and: P ∧ Q uall: [x:A]. B[x] member: t ∈ T guard: {T} nat: prop: ge: i ≥  decidable: Dec(P) or: P ∨ Q uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False not: ¬A top: Top
Lemmas referenced :  int_formula_prop_eq_lemma intformeq_wf decidable__equal_int swap_eval_2 nat_wf int_seg_wf equal_wf int_formula_prop_less_lemma intformless_wf 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 nat_properties lelt_wf int_seg_properties
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation cut dependent_set_memberEquality hypothesis equalitySymmetry independent_pairFormation lemma_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality setElimination rename hypothesisEquality applyEquality lambdaEquality setEquality intEquality productElimination dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality computeAll because_Cache independent_functionElimination

Latex:
\mforall{}n:\mBbbN{}.  \mforall{}i,j,k:\mBbbN{}n.    ((k  =  j)  {}\mRightarrow{}  ((swap\{n\}(i;j)  k)  =  i))



Date html generated: 2016_05_16-AM-07_29_52
Last ObjectModification: 2016_01_16-PM-10_06_14

Theory : perms_1


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