`∀I:Cname List. (I = [fresh-cname(I) / I]-[fresh-cname(I)] ∈ (Cname List))`

Proof

Definitions occuring in Statement :  fresh-cname: `fresh-cname(I)` cname_deq: `CnameDeq` coordinate_name: `Cname` list-diff: `as-bs` cons: `[a / b]` nil: `[]` list: `T List` all: `∀x:A. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` prop: `ℙ` so_apply: `x[s]` implies: `P `` Q` squash: `↓T` true: `True` subtype_rel: `A ⊆r B` uimplies: `b supposing a` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` top: `Top` deq: `EqDecider(T)` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A` rev_uimplies: `rev_uimplies(P;Q)`
Lemmas referenced :  list_wf coordinate_name_wf fresh-cname_wf set_wf not_wf l_member_wf equal_wf squash_wf true_wf list-diff-cons cname_deq_wf cons_wf nil_wf iff_weakening_equal deq_member_cons_lemma deq_member_nil_lemma bor_wf deq_wf bfalse_wf bool_wf eqtt_to_assert assert-deq-member strong-subtype-deq-subtype strong-subtype-set2 eqff_to_assert deq-member_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot list-diff-disjoint l_disjoint_singleton cons_member
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut hypothesis introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule lambdaEquality equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination applyEquality imageElimination universeEquality because_Cache setElimination rename natural_numberEquality imageMemberEquality baseClosed independent_isectElimination productElimination isect_memberEquality voidElimination voidEquality unionElimination equalityElimination setEquality dependent_set_memberEquality dependent_pairFormation promote_hyp instantiate cumulativity inlFormation

Latex:
\mforall{}I:Cname  List.  (I  =  [fresh-cname(I)  /  I]-[fresh-cname(I)])

Date html generated: 2017_10_05-AM-10_05_16
Last ObjectModification: 2017_07_28-AM-11_16_00

Theory : cubical!sets

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