### Nuprl Lemma : intlex-antisym

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

Proof

Definitions occuring in Statement :  intlex: `l1 ≤_lex l2` list: `T List` btrue: `tt` bool: `𝔹` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` intlex: `l1 ≤_lex l2` has-value: `(a)↓` nat: `ℕ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` prop: `ℙ` subtype_rel: `A ⊆r B` all: `∀x:A. B[x]` implies: `P `` 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 b then t else f fi ` assert: `↑b` false: `False` not: `¬A` bor: `p ∨bq` band: `p ∧b q` iff: `P `⇐⇒` Q` true: `True` rev_implies: `P `` 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

Latex:
\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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