### Nuprl Lemma : is-list-if-has-value-rec-snd

`∀[t:Base]. (is-list-if-has-value-rec(snd(t))) supposing (is-list-if-has-value-rec(t) and (t ~ <fst(t), snd(t)>))`

Proof

Definitions occuring in Statement :  is-list-if-has-value-rec: `is-list-if-has-value-rec(t)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` pi1: `fst(t)` pi2: `snd(t)` pair: `<a, b>` base: `Base` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` uimplies: `b supposing a` member: `t ∈ T` is-list-if-has-value-rec: `is-list-if-has-value-rec(t)` is-list-if-has-value-fun: `is-list-if-has-value-fun(t;n)` nat: `ℕ` ge: `i ≥ j ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ` has-value: `(a)↓` pi2: `snd(t)` sq_type: `SQType(T)` guard: `{T}` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` btrue: `tt` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` bfalse: `ff`
Lemmas referenced :  nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermAdd_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_wf le_wf primrec-unroll nat_wf is-list-if-has-value-rec_wf base_wf eq_int_wf intformeq_wf int_formula_prop_eq_lemma assert_wf bnot_wf not_wf equal-wf-T-base has-value_wf_base is-exception_wf add-subtract-cancel is-list-if-has-value-fun-ax-mem bool_cases subtype_base_sq bool_wf bool_subtype_base eqtt_to_assert assert_of_eq_int eqff_to_assert iff_transitivity iff_weakening_uiff assert_of_bnot
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut introduction sqequalAxiom hypothesis thin rename sqequalHypSubstitution sqequalRule isectElimination dependent_set_memberEquality addEquality setElimination hypothesisEquality natural_numberEquality extract_by_obid dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll because_Cache sqequalIntensionalEquality baseApply closedConclusion baseClosed equalityTransitivity equalitySymmetry divergentSqle sqleReflexivity instantiate cumulativity independent_functionElimination productElimination lambdaFormation impliesFunctionality

Latex:
\mforall{}[t:Base]
(is-list-if-has-value-rec(snd(t)))  supposing
(is-list-if-has-value-rec(t)  and
(t  \msim{}  <fst(t),  snd(t)>))

Date html generated: 2018_05_21-PM-10_19_32
Last ObjectModification: 2017_07_26-PM-06_37_03

Theory : eval!all

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