### Nuprl Lemma : list_match-aux-nil

`∀[bs:Top List]. ∀[used,R:Top].  list-match-aux([];bs;used;a,b.R[a;b])`

Proof

Definitions occuring in Statement :  list-match-aux: `list-match-aux(L1;L2;used;a,b.R[a; b])` nil: `[]` list: `T List` uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s1;s2]`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` list-match-aux: `list-match-aux(L1;L2;used;a,b.R[a; b])` sq_exists: `∃x:A [B[x]]` member: `t ∈ T` int_seg: `{i..j-}` lelt: `i ≤ j < k` and: `P ∧ Q` uimplies: `b supposing a` not: `¬A` implies: `P `` Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` all: `∀x:A. B[x]` top: `Top` prop: `ℙ` select: `L[n]` nil: `[]` it: `⋅` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` cand: `A c∧ B` inject: `Inj(A;B;f)` guard: `{T}` decidable: `Dec(P)` or: `P ∨ Q` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` so_apply: `x[s]`
Lemmas referenced :  length_of_nil_lemma full-omega-unsat intformand_wf intformless_wf itermVar_wf itermConstant_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_wf lelt_wf length_wf top_wf int_seg_wf stuck-spread base_wf int_seg_properties decidable__equal_int intformnot_wf intformeq_wf int_formula_prop_not_lemma int_formula_prop_eq_lemma equal_wf inject_wf all_wf not_wf l_member_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation dependent_set_memberFormation sqequalRule cut introduction extract_by_obid hypothesis lambdaEquality sqequalHypSubstitution setElimination thin rename dependent_set_memberEquality hypothesisEquality productElimination independent_pairFormation isectElimination natural_numberEquality independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality because_Cache baseClosed lambdaFormation equalityTransitivity equalitySymmetry applyLambdaEquality unionElimination productEquality functionExtensionality applyEquality

Latex:
\mforall{}[bs:Top  List].  \mforall{}[used,R:Top].    list-match-aux([];bs;used;a,b.R[a;b])

Date html generated: 2018_05_21-PM-00_46_41
Last ObjectModification: 2018_05_19-AM-06_49_49

Theory : list_1

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