Nuprl Lemma : coded-seq_wf

x:ℕ(coded-seq(x) ∈ k:ℕ × (ℕk ⟶ ℕ))


Proof




Definitions occuring in Statement :  coded-seq: coded-seq(x) int_seg: {i..j-} nat: all: x:A. B[x] member: t ∈ T function: x:A ⟶ B[x] product: x:A × B[x] natural_number: $n
Definitions unfolded in proof :  all: x:A. B[x] member: t ∈ T coded-seq: coded-seq(x) 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  le: A ≤ B less_than': less_than'(a;b) false: False not: ¬A prop: subtype_rel: A ⊆B bfalse: ff iff: ⇐⇒ Q rev_implies:  Q ge: i ≥  decidable: Dec(P) or: P ∨ Q satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] top: Top
Lemmas referenced :  eq_int_wf bool_wf uiff_transitivity equal-wf-T-base assert_wf eqtt_to_assert assert_of_eq_int false_wf le_wf int_seg_subtype_nat int_seg_wf nat_wf iff_transitivity bnot_wf not_wf iff_weakening_uiff eqff_to_assert assert_of_bnot coded-pair_wf subtract_wf nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermSubtract_wf itermVar_wf intformeq_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_eq_lemma int_formula_prop_wf itermAdd_wf int_term_value_add_lemma coded-seq1_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut sqequalRule introduction extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis natural_numberEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry baseClosed because_Cache intEquality independent_functionElimination productElimination independent_isectElimination dependent_pairEquality dependent_set_memberEquality independent_pairFormation lambdaEquality applyEquality functionEquality impliesFunctionality dependent_functionElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality computeAll productEquality addEquality

Latex:
\mforall{}x:\mBbbN{}.  (coded-seq(x)  \mmember{}  k:\mBbbN{}  \mtimes{}  (\mBbbN{}k  {}\mrightarrow{}  \mBbbN{}))



Date html generated: 2019_06_20-PM-02_40_28
Last ObjectModification: 2019_06_12-PM-00_28_29

Theory : num_thy_1


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