### Nuprl Lemma : name-morph-flips-commute

`∀I:Cname List. ∀x:name-morph(I;[]). ∀i,j:nameset(I).  (flip(flip(x;j);i) = flip(flip(x;i);j) ∈ name-morph(I;[]))`

Proof

Definitions occuring in Statement :  name-morph-flip: `flip(f;y)` name-morph: `name-morph(I;J)` nameset: `nameset(L)` coordinate_name: `Cname` nil: `[]` list: `T List` all: `∀x:A. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` name-morph-flip: `flip(f;y)` nameset: `nameset(L)` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` ifthenelse: `if b then t else f fi ` name-morph: `name-morph(I;J)` subtype_rel: `A ⊆r B` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` coordinate_name: `Cname` int_upper: `{i...}` squash: `↓T` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` prop: `ℙ` sq_stable: `SqStable(P)` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  name-morph-ext nil_wf coordinate_name_wf name-morph-flip_wf name-morph_wf eq-cname_wf bool_wf eqtt_to_assert assert-eq-cname extd-nameset-nil int_seg_wf int_seg_properties decidable__equal_int subtract_wf satisfiable-full-omega-tt intformnot_wf intformeq_wf itermSubtract_wf itermConstant_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_subtract_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf sq_stable__le sq_stable__l_member decidable__equal-coordinate_name decidable__le intformand_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_le_lemma decidable__lt intformless_wf int_formula_prop_less_lemma lelt_wf equal_wf eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot set_subtype_base int_subtype_base nsub2_subtype_extd-nameset
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis independent_isectElimination because_Cache sqequalRule setElimination rename unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination applyEquality natural_numberEquality applyLambdaEquality imageMemberEquality baseClosed imageElimination dependent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll dependent_set_memberEquality independent_pairFormation independent_functionElimination promote_hyp instantiate cumulativity

Latex:
\mforall{}I:Cname  List.  \mforall{}x:name-morph(I;[]).  \mforall{}i,j:nameset(I).    (flip(flip(x;j);i)  =  flip(flip(x;i);j))

Date html generated: 2017_10_05-AM-10_10_57
Last ObjectModification: 2017_07_28-AM-11_17_42

Theory : cubical!sets

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