Nuprl Lemma : assert-deq-disjoint

`∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[as,bs:A List].  uiff(↑deq-disjoint(eq;as;bs);l_disjoint(A;as;bs))`

Proof

Definitions occuring in Statement :  deq-disjoint: `deq-disjoint(eq;as;bs)` l_disjoint: `l_disjoint(T;l1;l2)` list: `T List` deq: `EqDecider(T)` assert: `↑b` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` universe: `Type`
Definitions unfolded in proof :  deq-disjoint: `deq-disjoint(eq;as;bs)` l_disjoint: `l_disjoint(T;l1;l2)` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` member: `t ∈ T` all: `∀x:A. B[x]` not: `¬A` implies: `P `` Q` false: `False` prop: `ℙ` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` so_apply: `x[s]` cand: `A c∧ B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` l_all: `(∀x∈L.P[x])` int_seg: `{i..j-}` guard: `{T}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` less_than: `a < b` squash: `↓T` subtype_rel: `A ⊆r B`
Lemmas referenced :  assert-deq-member assert_of_bnot l_all_functionality assert-bl-all iff_weakening_uiff iff_transitivity assert_witness deq_wf list_wf deq-disjoint_wf deq-member_wf bnot_wf bl-all_wf assert_wf uiff_wf l_disjoint_wf int_seg_wf int_formula_prop_less_lemma intformless_wf decidable__lt int_formula_prop_wf int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le length_wf int_seg_properties select_wf l_all_wf l_all_iff not_wf all_wf l_member_wf and_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut independent_pairFormation isect_memberFormation introduction lambdaFormation thin sqequalHypSubstitution productElimination lemma_by_obid isectElimination hypothesisEquality hypothesis independent_functionElimination voidElimination because_Cache sqequalRule lambdaEquality dependent_functionElimination functionEquality addLevel independent_isectElimination setElimination rename setEquality cumulativity natural_numberEquality unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidEquality computeAll imageElimination applyEquality universeEquality independent_pairEquality equalityTransitivity equalitySymmetry impliesFunctionality

Latex:
\mforall{}[A:Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[as,bs:A  List].    uiff(\muparrow{}deq-disjoint(eq;as;bs);l\_disjoint(A;as;bs))

Date html generated: 2016_05_14-PM-03_24_04
Last ObjectModification: 2016_01_14-PM-11_22_57

Theory : decidable!equality

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