Nuprl Lemma : last_append

[A,B:Top List].  last(A B) last(B) supposing ¬↑null(B)


Proof




Definitions occuring in Statement :  last: last(L) null: null(as) append: as bs list: List assert: b uimplies: supposing a uall: [x:A]. B[x] top: Top not: ¬A sqequal: t
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T all: x:A. B[x] nat: implies:  Q false: False ge: i ≥  uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] not: ¬A top: Top and: P ∧ Q prop: subtype_rel: A ⊆B guard: {T} or: P ∨ Q append: as bs so_lambda: so_lambda(x,y,z.t[x; y; z]) so_apply: x[s1;s2;s3] cons: [a b] colength: colength(L) so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] decidable: Dec(P) nil: [] it: so_lambda: λ2x.t[x] so_apply: x[s] sq_type: SQType(T) less_than: a < b squash: T less_than': less_than'(a;b) bool: 𝔹 unit: Unit btrue: tt uiff: uiff(P;Q) ifthenelse: if then else fi  bfalse: ff iff: ⇐⇒ Q rev_implies:  Q
Lemmas referenced :  nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma 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 not_wf assert_wf null_wf top_wf list_wf equal-wf-T-base nat_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases list_ind_nil_lemma product_subtype_list spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma decidable__le intformnot_wf int_formula_prop_not_lemma le_wf equal_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtype_base_sq set_subtype_base int_subtype_base decidable__equal_int list_ind_cons_lemma append_wf bool_wf bnot_wf last-cons uiff_transitivity eqtt_to_assert assert_of_null iff_transitivity iff_weakening_uiff eqff_to_assert assert_of_bnot append_is_nil
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination sqequalAxiom equalityTransitivity equalitySymmetry applyEquality because_Cache unionElimination promote_hyp hypothesis_subsumption productElimination applyLambdaEquality dependent_set_memberEquality addEquality baseClosed instantiate cumulativity imageElimination equalityElimination impliesFunctionality

Latex:
\mforall{}[A,B:Top  List].    last(A  @  B)  \msim{}  last(B)  supposing  \mneg{}\muparrow{}null(B)



Date html generated: 2017_04_17-AM-07_36_41
Last ObjectModification: 2017_02_27-PM-04_10_48

Theory : list_1


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