Nuprl Lemma : ml_insert_int-sq

[l:ℤ List]. ∀[x:ℤ].  (ml_insert_int(x;l) insert-int(x;l))


Proof




Definitions occuring in Statement :  ml_insert_int: ml_insert_int(x;l) insert-int: insert-int(x;l) list: List uall: [x:A]. B[x] int: 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 ≥  guard: {T} uimplies: supposing a prop: subtype_rel: A ⊆B or: P ∨ Q cons: [a b] colength: colength(L) so_lambda: λ2y.t[x; y] top: Top so_apply: x[s1;s2] squash: T sq_stable: SqStable(P) uiff: uiff(P;Q) and: P ∧ Q le: A ≤ B not: ¬A less_than': less_than'(a;b) true: True decidable: Dec(P) iff: ⇐⇒ Q rev_implies:  Q subtract: m nil: [] it: so_lambda: λ2x.t[x] so_apply: x[s] sq_type: SQType(T) less_than: a < b ml_insert_int: ml_insert_int(x;l) ml_apply: f(x) ifthenelse: if then else fi  btrue: tt spreadcons: spreadcons bfalse: ff insert-int: insert-int(x;l) so_lambda: so_lambda(x,y,z.t[x; y; z]) so_apply: x[s1;s2;s3] callbyvalueall: callbyvalueall has-value: (a)↓ has-valueall: has-valueall(a) bool: 𝔹 unit: Unit exists: x:A. B[x] bnot: ¬bb assert: b
Lemmas referenced :  nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf equal-wf-base nat_wf list_subtype_base int_subtype_base list_wf list-cases product_subtype_list spread_cons_lemma colength_wf_list sq_stable__le le_antisymmetry_iff add_functionality_wrt_le add-associates add-zero zero-add le-add-cancel equal-wf-T-base decidable__le false_wf not-le-2 condition-implies-le minus-add minus-one-mul minus-one-mul-top add-commutes le_wf equal_wf subtract_wf not-ge-2 less-iff-le minus-minus add-swap subtype_base_sq set_subtype_base insert_int_nil_lemma null_nil_lemma null_cons_lemma list_ind_cons_lemma valueall-type-has-valueall int-valueall-type evalall-reduce list-valueall-type lt_int_wf bool_wf assert_wf eqtt_to_assert assert_of_lt_int top_wf le-add-cancel2 eqff_to_assert bool_cases_sqequal bool_subtype_base assert-bnot cons_wf le_int_wf bnot_wf decidable__lt not-lt-2 uiff_transitivity assert_functionality_wrt_uiff bnot_of_lt_int assert_of_le_int value-type-has-value list-value-type insert-int_wf subtype_rel_self
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 independent_functionElimination voidElimination sqequalRule lambdaEquality dependent_functionElimination isect_memberEquality sqequalAxiom intEquality baseApply closedConclusion baseClosed applyEquality because_Cache unionElimination promote_hyp hypothesis_subsumption productElimination voidEquality applyLambdaEquality imageMemberEquality imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality equalityTransitivity equalitySymmetry instantiate cumulativity callbyvalueReduce equalityElimination lessCases dependent_pairFormation

Latex:
\mforall{}[l:\mBbbZ{}  List].  \mforall{}[x:\mBbbZ{}].    (ml\_insert\_int(x;l)  \msim{}  insert-int(x;l))



Date html generated: 2017_09_29-PM-05_51_21
Last ObjectModification: 2017_05_11-PM-05_14_11

Theory : ML


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