### Nuprl Lemma : list-max-aux_wf

`∀[T:Type]. ∀[f:T ⟶ ℤ]. ∀[L:T List].  (list-max-aux(x.f[x];L) ∈ i:ℤ × {x:T| f[x] = i ∈ ℤ}  + Top)`

Proof

Definitions occuring in Statement :  list-max-aux: `list-max-aux(x.f[x];L)` list: `T List` uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s]` member: `t ∈ T` set: `{x:A| B[x]} ` function: `x:A ⟶ B[x]` product: `x:A × B[x]` union: `left + right` int: `ℤ` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` list-max-aux: `list-max-aux(x.f[x];L)` so_apply: `x[s]` prop: `ℙ` top: `Top` so_lambda: `λ2x y.t[x; y]` has-value: `(a)↓` uimplies: `b supposing a` pi1: `fst(t)` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` and: `P ∧ Q` subtype_rel: `A ⊆r B` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A` so_apply: `x[s1;s2]`
Lemmas referenced :  list_accum_wf equal-wf-T-base top_wf value-type-has-value int-value-type lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int equal_wf int_subtype_base eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot less_than_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality unionEquality productEquality intEquality setEquality because_Cache hypothesis inrEquality isect_memberEquality voidElimination voidEquality lambdaEquality callbyvalueReduce independent_isectElimination applyEquality functionExtensionality unionElimination productElimination lambdaFormation equalityElimination inlEquality dependent_pairEquality dependent_set_memberEquality equalityTransitivity equalitySymmetry dependent_pairFormation promote_hyp dependent_functionElimination instantiate independent_functionElimination setElimination rename axiomEquality functionEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[f:T  {}\mrightarrow{}  \mBbbZ{}].  \mforall{}[L:T  List].    (list-max-aux(x.f[x];L)  \mmember{}  i:\mBbbZ{}  \mtimes{}  \{x:T|  f[x]  =  i\}    +  Top)

Date html generated: 2017_04_17-AM-07_40_25
Last ObjectModification: 2017_02_27-PM-04_13_57

Theory : list_1

Home Index