### Nuprl Lemma : extend-name-morph-irrelevant

`∀I,K:Cname List. ∀f:name-morph(I;K).  (f = f[fresh-cname(I):=fresh-cname(K)] ∈ name-morph(I;K))`

Proof

Definitions occuring in Statement :  extend-name-morph: `f[z1:=z2]` name-morph: `name-morph(I;J)` fresh-cname: `fresh-cname(I)` coordinate_name: `Cname` 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` extend-name-morph: `f[z1:=z2]` nameset: `nameset(L)` subtype_rel: `A ⊆r B` prop: `ℙ` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` ifthenelse: `if b then t else f fi ` not: `¬A` false: `False` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` name-morph: `name-morph(I;J)`
Lemmas referenced :  name-morphs-equal eq-cname_wf fresh-cname_wf coordinate_name_wf not_wf l_member_wf bool_wf eqtt_to_assert assert-eq-cname fresh-cname-not-equal2 eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot nameset_wf name-morph_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality functionExtensionality sqequalRule setElimination rename hypothesis applyEquality lambdaEquality setEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination dependent_functionElimination independent_functionElimination voidElimination dependent_pairFormation promote_hyp instantiate cumulativity because_Cache

Latex:
\mforall{}I,K:Cname  List.  \mforall{}f:name-morph(I;K).    (f  =  f[fresh-cname(I):=fresh-cname(K)])

Date html generated: 2017_10_05-AM-10_08_46
Last ObjectModification: 2017_07_28-AM-11_17_01

Theory : cubical!sets

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