Nuprl Lemma : code-pair_wf

[a,b:ℕ].  (code-pair(a;b) ∈ ℕ)


Proof




Definitions occuring in Statement :  code-pair: code-pair(a;b) nat: uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T code-pair: code-pair(a;b) nat: ge: i ≥  all: x:A. B[x] decidable: Dec(P) or: P ∨ Q uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False implies:  Q not: ¬A top: Top and: P ∧ Q prop: subtype_rel: A ⊆B guard: {T} uiff: uiff(P;Q)
Lemmas referenced :  triangular-num_wf 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 add_nat_wf nat_wf add-is-int-iff intformeq_wf int_formula_prop_eq_lemma false_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule dependent_set_memberEquality addEquality extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename because_Cache hypothesis hypothesisEquality dependent_functionElimination unionElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll applyEquality lambdaFormation equalityTransitivity equalitySymmetry applyLambdaEquality pointwiseFunctionality promote_hyp baseApply closedConclusion baseClosed productElimination independent_functionElimination axiomEquality

Latex:
\mforall{}[a,b:\mBbbN{}].    (code-pair(a;b)  \mmember{}  \mBbbN{})



Date html generated: 2019_06_20-PM-02_39_08
Last ObjectModification: 2019_06_12-PM-01_16_28

Theory : num_thy_1


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