### Nuprl Lemma : assert-face-name-eq

`∀[I:Cname List]. ∀[a,b:nameset(I) × ℕ2].  uiff(↑face-name-eq(a;b);a = b ∈ (nameset(I) × ℕ2))`

Proof

Definitions occuring in Statement :  face-name-eq: `face-name-eq(a;b)` nameset: `nameset(L)` coordinate_name: `Cname` list: `T List` int_seg: `{i..j-}` assert: `↑b` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` product: `x:A × B[x]` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  nameset: `nameset(L)` face-name-eq: `face-name-eq(a;b)` coordinate_name: `Cname` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` so_apply: `x[s]` all: `∀x:A. B[x]` sq_type: `SQType(T)` implies: `P `` Q` guard: `{T}` prop: `ℙ` int_upper: `{i...}` int_seg: `{i..j-}` subtype_rel: `A ⊆r B` deq: `EqDecider(T)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  subtype_base_sq product_subtype_base int_subtype_base equal_wf subtype_rel_product int_upper_wf l_member_wf int_seg_wf set_wf equal_functionality_wrt_subtype_rel2 assert_wf product-deq_wf int-deq_wf uiff_wf deq_wf list_wf assert_witness iff_weakening_uiff assert-product-deq
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep independent_pairFormation isect_memberFormation cut thin instantiate introduction extract_by_obid sqequalHypSubstitution isectElimination cumulativity productEquality intEquality independent_isectElimination because_Cache lambdaEquality hypothesis lambdaFormation dependent_functionElimination independent_functionElimination hypothesisEquality productElimination independent_pairEquality setElimination rename setEquality natural_numberEquality dependent_set_memberEquality applyEquality isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry addLevel

Latex:
\mforall{}[I:Cname  List].  \mforall{}[a,b:nameset(I)  \mtimes{}  \mBbbN{}2].    uiff(\muparrow{}face-name-eq(a;b);a  =  b)

Date html generated: 2017_10_05-AM-10_17_30
Last ObjectModification: 2017_07_28-AM-11_20_20

Theory : cubical!sets

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