### Nuprl Lemma : last-reverse

`∀[T:Type]. ∀[L:T List].  (last(rev(L)) ~ hd(L))`

Proof

Definitions occuring in Statement :  last: `last(L)` reverse: `rev(as)` hd: `hd(l)` list: `T List` uall: `∀[x:A]. B[x]` universe: `Type` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` or: `P ∨ Q` nil: `[]` hd: `hd(l)` it: `⋅` last: `last(L)` select: `L[n]` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` cons: `[a / b]` le: `A ≤ B` less_than': `less_than'(a;b)` colength: `colength(L)` guard: `{T}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` less_than: `a < b` squash: `↓T` decidable: `Dec(P)` subtype_rel: `A ⊆r B` assert: `↑b` ifthenelse: `if b then t else f fi ` bfalse: `ff` subtract: `n - m`
Lemmas referenced :  nat_properties full-omega-unsat intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf istype-int int_formula_prop_and_lemma istype-void int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf list-cases reverse_nil_lemma pi1-axiom stuck-spread istype-base product_subtype_list colength-cons-not-zero colength_wf_list istype-false le_wf subtract-1-ge-0 subtype_base_sq intformeq_wf int_formula_prop_eq_lemma set_subtype_base int_subtype_base spread_cons_lemma decidable__equal_int subtract_wf intformnot_wf itermSubtract_wf itermAdd_wf int_formula_prop_not_lemma int_term_value_subtract_lemma int_term_value_add_lemma decidable__le reverse-cons reduce_hd_cons_lemma last_append reverse_wf subtype_rel_list top_wf istype-universe cons_wf nil_wf null_cons_lemma length_of_cons_lemma length_of_nil_lemma nat_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut thin Error :lambdaFormation_alt,  extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination approximateComputation independent_functionElimination Error :dependent_pairFormation_alt,  Error :lambdaEquality_alt,  int_eqEquality dependent_functionElimination Error :isect_memberEquality_alt,  voidElimination sqequalRule independent_pairFormation Error :universeIsType,  axiomSqEquality Error :functionIsTypeImplies,  Error :inhabitedIsType,  unionElimination baseClosed promote_hyp hypothesis_subsumption productElimination Error :equalityIsType1,  because_Cache Error :dependent_set_memberEquality_alt,  instantiate equalityTransitivity equalitySymmetry applyLambdaEquality imageElimination Error :equalityIsType4,  baseApply closedConclusion applyEquality intEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].    (last(rev(L))  \msim{}  hd(L))

Date html generated: 2019_06_20-PM-01_46_48
Last ObjectModification: 2018_10_07-AM-00_05_31

Theory : list_1

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