### Nuprl Lemma : sq-decider-list-deq

`∀[eq:Base]. sq-decider(list-deq(eq)) supposing sq-decider(eq)`

Proof

Definitions occuring in Statement :  list-deq: `list-deq(eq)` sq-decider: `sq-decider(eq)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` base: `Base`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` sq-decider: `sq-decider(eq)` implies: `P `` Q` exists: `∃x:A. B[x]` list-deq: `list-deq(eq)` list_ind: list_ind nat: `ℕ` false: `False` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` not: `¬A` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` decidable: `Dec(P)` or: `P ∨ Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]` nat_plus: `ℕ+` has-value: `(a)↓` band: `p ∧b q` bfalse: `ff` ifthenelse: `if b then t else f fi ` outl: `outl(x)` cand: `A c∧ B` sq_type: `SQType(T)` guard: `{T}` true: `True` null: `null(as)` btrue: `tt`
Lemmas referenced :  value-type-has-value base_wf union-value-type nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf has-value_wf_base int_subtype_base fun_exp0_lemma strictness-apply bottom_diverge decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma exists_wf sqequal-wf-base sq-decider_wf fun_exp_unroll_1 has-value-implies-dec-ispair-2 top_wf equal_wf subtype_base_sq has-value-implies-dec-isaxiom-2 subtype_rel_self
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaFormation sqequalHypSubstitution productElimination thin sqequalRule hypothesis extract_by_obid isectElimination unionEquality voidEquality independent_isectElimination inlEquality hypothesisEquality compactness setElimination rename intWeakElimination natural_numberEquality dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry sqequalIntensionalEquality baseApply closedConclusion baseClosed because_Cache applyEquality unionElimination sqequalAxiom dependent_set_memberEquality callbyvalueApply callbyvalueCallbyvalue callbyvalueReduce callbyvalueDecide instantiate cumulativity promote_hyp addLevel levelHypothesis callbyvalueIspair

Latex:
\mforall{}[eq:Base].  sq-decider(list-deq(eq))  supposing  sq-decider(eq)

Date html generated: 2017_09_29-PM-06_04_19
Last ObjectModification: 2017_07_26-PM-02_53_03

Theory : decidable!equality

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