### Nuprl Lemma : swap-names_wf

`∀[I:Cname List]. ∀[z1,z2:nameset(I)].  (swap-names(z1;z2) ∈ name-morph(I;I))`

Proof

Definitions occuring in Statement :  swap-names: `swap-names(z1;z2)` name-morph: `name-morph(I;J)` nameset: `nameset(L)` coordinate_name: `Cname` list: `T List` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` swap-names: `swap-names(z1;z2)` name-morph: `name-morph(I;J)` nameset: `nameset(L)` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` subtype_rel: `A ⊆r B` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A` coordinate_name: `Cname` int_upper: `{i...}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` squash: `↓T` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` le: `A ≤ B`
Lemmas referenced :  nameset_wf list_wf coordinate_name_wf eq-cname_wf bool_wf eqtt_to_assert assert-eq-cname nameset_subtype_extd-nameset eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot l_member_wf extd-nameset_wf true_wf isname-nameset set_subtype_base le_wf int_subtype_base extd-nameset_subtype_base decidable__equal_int satisfiable-full-omega-tt intformnot_wf intformeq_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_formula_prop_wf equal-wf-base all_wf assert_wf isname_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule dependent_set_memberEquality sqequalHypSubstitution hypothesis axiomEquality equalityTransitivity equalitySymmetry extract_by_obid isectElimination thin hypothesisEquality isect_memberEquality because_Cache lambdaEquality setElimination rename lambdaFormation unionElimination equalityElimination productElimination independent_isectElimination applyEquality dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination intEquality natural_numberEquality applyLambdaEquality imageMemberEquality baseClosed imageElimination int_eqEquality voidEquality computeAll functionEquality functionExtensionality

Latex:
\mforall{}[I:Cname  List].  \mforall{}[z1,z2:nameset(I)].    (swap-names(z1;z2)  \mmember{}  name-morph(I;I))

Date html generated: 2017_10_05-AM-10_09_04
Last ObjectModification: 2017_07_28-AM-11_17_04

Theory : cubical!sets

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