### Nuprl Lemma : bl-exists-as-accum

`∀[T:Type]. ∀[L:T List]. ∀[P:T ⟶ 𝔹].`
`  ((∃x∈L.P[x])_b ~ accumulate (with value p and list item x):`
`                    p ∨bP[x]`
`                   over list:`
`                     L`
`                   with starting value:`
`                    ff))`

Proof

Definitions occuring in Statement :  bl-exists: `(∃x∈L.P[x])_b` list_accum: list_accum list: `T List` bor: `p ∨bq` bfalse: `ff` bool: `𝔹` uall: `∀[x:A]. B[x]` so_apply: `x[s]` function: `x:A ⟶ B[x]` universe: `Type` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` bl-exists: `(∃x∈L.P[x])_b` squash: `↓T` prop: `ℙ` so_apply: `x[s]` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` top: `Top` true: `True` subtype_rel: `A ⊆r B` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` false: `False` bor: `p ∨bq` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]`
Lemmas referenced :  subtype_base_sq bool_wf bool_subtype_base equal_wf squash_wf true_wf reduce-as-accum bor_wf eqtt_to_assert testxxx_lemma bor_tt_simp btrue_wf iff_weakening_equal eqff_to_assert bool_cases_sqequal assert-bnot bfalse_wf list_accum_wf list_wf bor_ff_simp
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin instantiate extract_by_obid sqequalHypSubstitution isectElimination cumulativity hypothesis independent_isectElimination applyEquality lambdaEquality imageElimination hypothesisEquality equalityTransitivity equalitySymmetry because_Cache functionExtensionality sqequalRule lambdaFormation unionElimination equalityElimination productElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality natural_numberEquality imageMemberEquality baseClosed independent_functionElimination dependent_pairFormation promote_hyp universeEquality sqequalAxiom functionEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbB{}].
((\mexists{}x\mmember{}L.P[x])\_b  \msim{}  accumulate  (with  value  p  and  list  item  x):
p  \mvee{}\msubb{}P[x]
over  list:
L
with  starting  value:
ff))

Date html generated: 2017_04_17-AM-08_03_30
Last ObjectModification: 2017_02_27-PM-04_33_38

Theory : list_1

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