### Nuprl Lemma : poset-cat-arrow-flip

`∀I:Cname List. ∀x:cat-ob(poset-cat(I)). ∀a:nameset(I).  (((x a) = 0 ∈ ℤ) `` (cat-arrow(poset-cat(I)) x flip(x;a)))`

Proof

Definitions occuring in Statement :  poset-cat: `poset-cat(J)` name-morph-flip: `flip(f;y)` nameset: `nameset(L)` coordinate_name: `Cname` cat-arrow: `cat-arrow(C)` cat-ob: `cat-ob(C)` list: `T List` all: `∀x:A. B[x]` implies: `P `` Q` apply: `f a` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` name-morph-flip: `flip(f;y)` poset-cat: `poset-cat(J)` cat-arrow: `cat-arrow(C)` pi2: `snd(t)` pi1: `fst(t)` uall: `∀[x:A]. B[x]` member: `t ∈ T` subtype_rel: `A ⊆r B` nameset: `nameset(L)` 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` 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` rev_uimplies: `rev_uimplies(P;Q)` coordinate_name: `Cname` int_upper: `{i...}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` le: `A ≤ B` less_than': `less_than'(a;b)` subtract: `n - m` sq_stable: `SqStable(P)` squash: `↓T` cat-ob: `cat-ob(C)` name-morph: `name-morph(I;J)` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top`
Lemmas referenced :  assert_of_le_int eq-cname_wf bool_wf eqtt_to_assert assert-eq-cname subtract_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot coordinate_name_wf set_subtype_base le_wf int_subtype_base false_wf sq_stable__l_member decidable__equal-coordinate_name sq_stable__le decidable__le nameset_wf extd-nameset_wf nil_wf all_wf assert_wf isname_wf l_member_wf satisfiable-full-omega-tt intformnot_wf intformle_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_wf equal-wf-T-base cat-ob_wf poset-cat_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation sqequalRule cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin applyEquality because_Cache hypothesisEquality hypothesis setElimination rename unionElimination equalityElimination productElimination independent_isectElimination natural_numberEquality equalityTransitivity equalitySymmetry dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination intEquality lambdaEquality independent_pairFormation imageMemberEquality baseClosed imageElimination setEquality functionEquality functionExtensionality dependent_set_memberEquality int_eqEquality isect_memberEquality voidEquality computeAll

Latex:
\mforall{}I:Cname  List.  \mforall{}x:cat-ob(poset-cat(I)).  \mforall{}a:nameset(I).
(((x  a)  =  0)  {}\mRightarrow{}  (cat-arrow(poset-cat(I))  x  flip(x;a)))

Date html generated: 2017_10_05-AM-10_27_48
Last ObjectModification: 2017_07_28-AM-11_23_20

Theory : cubical!sets

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