### Nuprl Lemma : decidable__squash-list-match-ext

`∀[A,B:Type]. ∀[R:A ⟶ B ⟶ ℙ].`
`  ((∀a:A. ∀b:B.  Dec(R[a;b])) `` (∀as:A List. ∀bs:B List.  Dec(↓list-match(as;bs;a,b.R[a;b]))))`

Proof

Definitions occuring in Statement :  list-match: `list-match(L1;L2;a,b.R[a; b])` list: `T List` decidable: `Dec(P)` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` all: `∀x:A. B[x]` squash: `↓T` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  member: `t ∈ T` ifthenelse: `if b then t else f fi ` it: `⋅` btrue: `tt` let: let uall: `∀[x:A]. B[x]` uimplies: `b supposing a` unit: `Unit` sq_type: `SQType(T)` all: `∀x:A. B[x]` implies: `P `` Q` guard: `{T}` decidable__squash-list-match decidable__squash-list-match-aux-ext
Lemmas referenced :  decidable__squash-list-match subtype_base_sq unit_wf2 unit_subtype_base trivial-equal decidable__squash-list-match-aux-ext
Rules used in proof :  introduction sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut instantiate extract_by_obid hypothesis sqequalRule thin sqequalHypSubstitution equalityTransitivity equalitySymmetry isectElimination cumulativity independent_isectElimination axiomEquality natural_numberEquality dependent_functionElimination independent_functionElimination because_Cache

Latex:
\mforall{}[A,B:Type].  \mforall{}[R:A  {}\mrightarrow{}  B  {}\mrightarrow{}  \mBbbP{}].
((\mforall{}a:A.  \mforall{}b:B.    Dec(R[a;b]))  {}\mRightarrow{}  (\mforall{}as:A  List.  \mforall{}bs:B  List.    Dec(\mdownarrow{}list-match(as;bs;a,b.R[a;b]))))

Date html generated: 2018_05_21-PM-00_50_17
Last ObjectModification: 2018_05_19-AM-06_51_35

Theory : list_1

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