### Nuprl Lemma : name-morph-extend_wf

`∀[I,J:Cname List]. ∀[f:name-morph(I;J)].  ((f)+ ∈ name-morph(I+;J+))`

Proof

Definitions occuring in Statement :  name-morph-extend: `(f)+` name-morph: `name-morph(I;J)` add-fresh-cname: `I+` 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` name-morph-extend: `(f)+` add-fresh-cname: `I+` all: `∀x:A. B[x]` implies: `P `` Q` uimplies: `b supposing a` has-value: `(a)↓` name-morph: `name-morph(I;J)` cname_deq: `CnameDeq` top: `Top` nameset: `nameset(L)` coordinate_name: `Cname` int_upper: `{i...}` 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]` subtype_rel: `A ⊆r B` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` prop: `ℙ` nequal: `a ≠ b ∈ T ` squash: `↓T` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` isname: `isname(z)` true: `True` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  fresh-cname_wf name-morph_wf list_wf coordinate_name_wf value-type-has-value coordinate_name-value-type extd-nameset_subtype cons_wf l_subset_right_cons_trivial nameset_wf intdeq_reduce_lemma istype-void eq_int_wf eqtt_to_assert assert_of_eq_int eqff_to_assert bool_subtype_base bool_cases_sqequal subtype_base_sq bool_wf assert-bnot neg_assert_of_eq_int cons_member l_member_wf nameset_subtype_extd-nameset full-omega-unsat intformand_wf intformnot_wf intformeq_wf itermVar_wf istype-int int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_formula_prop_wf iff_imp_equal_bool le_int_wf btrue_wf iff_functionality_wrt_iff assert_wf le_wf true_wf iff_weakening_uiff assert_of_le_int iff_weakening_equal istype-assert int_subtype_base extd-nameset_wf set_subtype_base isname_wf extd-nameset_subtype_base assert-isname nameset_subtype
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis inhabitedIsType lambdaFormation_alt setElimination rename equalityIsType1 equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination sqequalRule axiomEquality universeIsType isect_memberEquality_alt isectIsTypeImplies independent_isectElimination because_Cache callbyvalueReduce dependent_set_memberEquality_alt lambdaEquality_alt voidElimination unionElimination equalityElimination productElimination dependent_pairFormation_alt equalityIsType3 applyEquality promote_hyp instantiate cumulativity inlFormation_alt applyLambdaEquality imageMemberEquality baseClosed imageElimination natural_numberEquality approximateComputation int_eqEquality independent_pairFormation intEquality equalityIsType4 closedConclusion equalityIsType2 functionIsType

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

Date html generated: 2019_11_05-PM-00_24_24
Last ObjectModification: 2018_11_08-PM-00_03_22

Theory : cubical!sets

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