Nuprl Lemma : intlex-antisym

[l1,l2:ℤ List].  (l1 l2 ∈ (ℤ List)) supposing (l2 ≤_lex l1 tt and l1 ≤_lex l2 tt)


Definitions occuring in Statement :  intlex: l1 ≤_lex l2 list: List btrue: tt bool: 𝔹 uimplies: supposing a uall: [x:A]. B[x] int: equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a intlex: l1 ≤_lex l2 has-value: (a)↓ nat: so_lambda: λ2x.t[x] so_apply: x[s] prop: subtype_rel: A ⊆B all: x:A. B[x] implies:  Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) and: P ∧ Q top: Top bfalse: ff exists: x:A. B[x] or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb ifthenelse: if then else fi  assert: b false: False not: ¬A bor: p ∨bq band: p ∧b q iff: ⇐⇒ Q true: True rev_implies:  Q squash: T
Lemmas referenced :  value-type-has-value nat_wf set-value-type le_wf int-value-type length_wf_nat equal-wf-base bool_wf list_subtype_base int_subtype_base list_wf lt_int_wf length_wf eqtt_to_assert assert_of_lt_int testxxx_lemma eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot less_than_wf less_than_transitivity2 le_weakening2 less_than_irreflexivity eq_int_wf assert_of_eq_int less_than_transitivity1 le_weakening neg_assert_of_eq_int btrue_neq_bfalse iff_imp_equal_bool intlex-aux_wf assert_wf and_wf squash_wf true_wf eq_int_eq_true iff_weakening_equal band_wf intlex-aux-antisym
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution sqequalRule callbyvalueReduce extract_by_obid isectElimination thin hypothesis independent_isectElimination intEquality lambdaEquality natural_numberEquality hypothesisEquality baseApply closedConclusion baseClosed applyEquality because_Cache isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry lambdaFormation unionElimination equalityElimination productElimination dependent_functionElimination voidElimination voidEquality dependent_pairFormation promote_hyp instantiate cumulativity independent_functionElimination dependent_set_memberEquality independent_pairFormation applyLambdaEquality setElimination rename imageElimination universeEquality equalityUniverse levelHypothesis imageMemberEquality

\mforall{}[l1,l2:\mBbbZ{}  List].    (l1  =  l2)  supposing  (l2  \mleq{}\_lex  l1  =  tt  and  l1  \mleq{}\_lex  l2  =  tt)

Date html generated: 2017_09_29-PM-05_49_24
Last ObjectModification: 2017_07_26-PM-01_37_42

Theory : list_0

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