### Nuprl Lemma : name-morph-flip-flip

`∀I:Cname List. ∀f:name-morph(I;[]). ∀j:nameset(I).  (flip(flip(f;j);j) = f ∈ 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 ` 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` subtype_rel: `A ⊆r B` name-morph: `name-morph(I;J)` int_seg: `{i..j-}` lelt: `i ≤ j < k` coordinate_name: `Cname` int_upper: `{i...}` squash: `↓T` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` sq_stable: `SqStable(P)`
Lemmas referenced :  name-morph-ext nil_wf coordinate_name_wf name-morph-flip_wf eq-cname_wf bool_wf eqtt_to_assert assert-eq-cname eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot nameset_wf name-morph_wf list_wf 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 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 sqequalRule setElimination rename unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination because_Cache voidElimination applyEquality natural_numberEquality applyLambdaEquality imageMemberEquality baseClosed imageElimination lambdaEquality int_eqEquality intEquality isect_memberEquality voidEquality computeAll dependent_set_memberEquality independent_pairFormation

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

Date html generated: 2017_10_05-AM-10_11_07
Last ObjectModification: 2017_07_28-AM-11_17_46

Theory : cubical!sets

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