Nuprl Lemma : code-coded-seq1

[k:ℕ+]. ∀[x:ℕ].  (code-seq1(k;λn.coded-seq1(k 1;x;n)) x ∈ ℤ)


Proof




Definitions occuring in Statement :  coded-seq1: coded-seq1(k;x;n) code-seq1: code-seq1(k;s) nat_plus: + nat: uall: [x:A]. B[x] lambda: λx.A[x] subtract: m natural_number: $n int: equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T code-seq1: code-seq1(k;s) primrec: primrec(n;b;c) subtract: m ifthenelse: if then else fi  eq_int: (i =z j) btrue: tt coded-seq1: coded-seq1(k;x;n) nat: all: x:A. B[x] nat_plus: + implies:  Q bool: 𝔹 unit: Unit it: uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a ge: i ≥  not: ¬A satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False top: Top prop: bfalse: ff or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b so_lambda: λ2x.t[x] decidable: Dec(P) int_seg: {i..j-} lelt: i ≤ j < k subtype_rel: A ⊆B so_apply: x[s] nequal: a ≠ b ∈  squash: T label: ...$L... t true: True iff: ⇐⇒ Q
Lemmas referenced :  nat_wf nat_plus_properties add-subtract-cancel eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int nat_properties full-omega-unsat intformand_wf intformeq_wf itermVar_wf itermConstant_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_less_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int coded-pair_wf uall_wf code-seq1_wf decidable__le intformnot_wf intformle_wf int_formula_prop_not_lemma int_formula_prop_le_lemma le_wf coded-seq1_wf subtract_wf int_seg_properties itermSubtract_wf int_term_value_subtract_lemma subtract-add-cancel decidable__lt lelt_wf int_seg_wf nat_plus_wf primrec-wf-nat-plus nat_plus_subtype_nat primrec-unroll lt_int_wf assert_of_lt_int itermAdd_wf int_term_value_add_lemma less_than_wf decidable__equal_int int_subtype_base coded-code-pair code-pair_wf squash_wf true_wf code-coded-pair subtype_rel_self iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule hypothesis sqequalHypSubstitution setElimination thin rename hypothesisEquality extract_by_obid lambdaFormation isectElimination natural_numberEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation promote_hyp instantiate cumulativity because_Cache productEquality dependent_set_memberEquality addEquality applyEquality axiomEquality hyp_replacement applyLambdaEquality functionExtensionality spreadEquality imageElimination universeEquality imageMemberEquality baseClosed

Latex:
\mforall{}[k:\mBbbN{}\msupplus{}].  \mforall{}[x:\mBbbN{}].    (code-seq1(k;\mlambda{}n.coded-seq1(k  -  1;x;n))  =  x)



Date html generated: 2019_06_20-PM-02_40_06
Last ObjectModification: 2019_06_12-PM-00_28_09

Theory : num_thy_1


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