### Nuprl Lemma : name-morph-inv_wf

`∀[I,J:Cname List]. ∀[f:name-morph(I;J)].  (name-morph-inv(I;f) ∈ name-morph-range(f;I) ⟶ nameset(I))`

Proof

Definitions occuring in Statement :  name-morph-inv: `name-morph-inv(I;f)` name-morph-range: `name-morph-range(f;I)` name-morph: `name-morph(I;J)` nameset: `nameset(L)` coordinate_name: `Cname` list: `T List` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` name-morph-inv: `name-morph-inv(I;f)` name-morph-range: `name-morph-range(f;I)` exists: `∃x:A. B[x]` name-morph: `name-morph(I;J)` subtype_rel: `A ⊆r B` coordinate_name: `Cname` int_upper: `{i...}` nameset: `nameset(L)` and: `P ∧ Q` all: `∀x:A. B[x]` prop: `ℙ` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` implies: `P `` Q` cand: `A c∧ B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` band: `p ∧b q` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` uimplies: `b supposing a` guard: `{T}` bfalse: `ff` squash: `↓T` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` not: `¬A` top: `Top` cons: `[a / b]`
Lemmas referenced :  name-morph-range_wf name-morph_wf list_wf coordinate_name_wf band_wf isname_wf eq_int_wf extd-nameset_subtype_int nameset_wf list-subtype member_filter_2 l_member_wf l_member-settype iff_transitivity assert_wf bool_wf eqtt_to_assert equal_wf iff_weakening_uiff assert_of_band assert_of_eq_int decidable__equal_int satisfiable-full-omega-tt intformand_wf intformnot_wf intformeq_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_formula_prop_wf filter_wf5 list-cases hd_wf member-implies-null-eq-bfalse null_nil_lemma btrue_wf btrue_neq_bfalse product_subtype_list length_cons_ge_one subtype_rel_list top_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaEquality sqequalHypSubstitution setElimination thin rename productElimination hypothesis extract_by_obid isectElimination hypothesisEquality sqequalRule axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache applyEquality dependent_functionElimination setEquality dependent_set_memberEquality independent_functionElimination independent_pairFormation lambdaFormation unionElimination equalityElimination independent_isectElimination productEquality intEquality applyLambdaEquality imageMemberEquality baseClosed imageElimination natural_numberEquality dependent_pairFormation int_eqEquality voidElimination voidEquality computeAll promote_hyp hypothesis_subsumption

Latex:
\mforall{}[I,J:Cname  List].  \mforall{}[f:name-morph(I;J)].
(name-morph-inv(I;f)  \mmember{}  name-morph-range(f;I)  {}\mrightarrow{}  nameset(I))

Date html generated: 2017_10_05-AM-10_06_02
Last ObjectModification: 2017_07_28-AM-11_16_14

Theory : cubical!sets

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