Nuprl Lemma : code-coded-seq

x:ℕ(let k,s coded-seq(x) in code-seq(k;s) x ∈ ℤ)


Proof




Definitions occuring in Statement :  coded-seq: coded-seq(x) code-seq: code-seq(k;s) nat: all: x:A. B[x] spread: spread def int: equal: t ∈ T
Definitions unfolded in proof :  all: x:A. B[x] coded-seq: coded-seq(x) member: t ∈ T uall: [x:A]. B[x] nat: implies:  Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a ifthenelse: if then else fi  bfalse: ff exists: x:A. B[x] prop: or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b false: False le: A ≤ B less_than': less_than'(a;b) not: ¬A ge: i ≥  int_upper: {i...} code-seq: code-seq(k;s) eq_int: (i =z j) decidable: Dec(P) satisfiable_int_formula: satisfiable_int_formula(fmla) top: Top nat_plus: + nequal: a ≠ b ∈  iff: ⇐⇒ Q rev_implies:  Q subtract: m subtype_rel: A ⊆B true: True squash: T label: ...$L... t
Lemmas referenced :  eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int int_upper_subtype_nat false_wf le_wf nat_properties nequal-le-implies zero-add nat_wf int_subtype_base coded-pair_wf subtract_wf int_upper_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermSubtract_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_subtract_lemma int_term_value_var_lemma int_formula_prop_wf intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma add-subtract-cancel code-coded-seq1 decidable__lt not-lt-2 not-equal-2 condition-implies-le minus-add minus-one-mul minus-one-mul-top add-commutes add_functionality_wrt_le add-associates add-zero le-add-cancel less_than_wf decidable__equal_int coded-code-pair code-pair_wf squash_wf true_wf code-coded-pair iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis natural_numberEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination sqequalRule dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination because_Cache voidElimination hypothesis_subsumption dependent_set_memberEquality independent_pairFormation intEquality lambdaEquality int_eqEquality isect_memberEquality voidEquality computeAll productEquality addEquality hyp_replacement applyLambdaEquality applyEquality minusEquality imageElimination universeEquality imageMemberEquality baseClosed

Latex:
\mforall{}x:\mBbbN{}.  (let  k,s  =  coded-seq(x)  in  code-seq(k;s)  =  x)



Date html generated: 2019_06_20-PM-02_40_36
Last ObjectModification: 2019_06_12-PM-00_28_33

Theory : num_thy_1


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