### Nuprl Lemma : guarded_permutation_transitivity

`∀[T:Type]. ∀[P:L:(T List) ⟶ ℕ||L|| - 1 ⟶ ℙ].  Trans(T List)(_1 guarded_permutation(T;P) _2)`

Proof

Definitions occuring in Statement :  guarded_permutation: `guarded_permutation(T;P)` length: `||as||` list: `T List` trans: `Trans(T;x,y.E[x; y])` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` prop: `ℙ` infix_ap: `x f y` function: `x:A ⟶ B[x]` subtract: `n - m` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` guarded_permutation: `guarded_permutation(T;P)` trans: `Trans(T;x,y.E[x; y])` all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` so_lambda: `λ2x.t[x]` prop: `ℙ` and: `P ∧ Q` subtype_rel: `A ⊆r B` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` false: `False` less_than: `a < b` squash: `↓T` uiff: `uiff(P;Q)` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` subtract: `n - m` so_apply: `x[s]`
Lemmas referenced :  rel_star_transitivity exists_wf int_seg_wf subtract_wf length_wf equal_wf swap_wf decidable__lt subtract-is-int-iff satisfiable-full-omega-tt intformand_wf intformnot_wf intformless_wf itermVar_wf itermSubtract_wf itermConstant_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_subtract_lemma int_term_value_constant_lemma int_formula_prop_wf false_wf lelt_wf add-member-int_seg2 decidable__le intformle_wf int_formula_prop_le_lemma infix_ap_wf list_wf rel_star_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin because_Cache lambdaEquality natural_numberEquality hypothesisEquality hypothesis sqequalRule productEquality applyEquality functionExtensionality setElimination rename dependent_set_memberEquality productElimination independent_pairFormation dependent_functionElimination cumulativity unionElimination pointwiseFunctionality equalityTransitivity equalitySymmetry promote_hyp imageElimination baseApply closedConclusion baseClosed independent_isectElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll independent_functionElimination instantiate universeEquality functionEquality

Latex:
\mforall{}[T:Type].  \mforall{}[P:L:(T  List)  {}\mrightarrow{}  \mBbbN{}||L||  -  1  {}\mrightarrow{}  \mBbbP{}].    Trans(T  List)(\$_{1}\$  guarded\_per\000Cmutation(T;P)  \$_{2}\$)

Date html generated: 2017_10_01-AM-08_38_35
Last ObjectModification: 2017_07_26-PM-04_27_05

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