### Nuprl Lemma : equal-nat-inf-infinity2

`∀[x:ℕ∞]. uiff(x = ∞ ∈ ℕ∞;∀i:ℕ. (↑(x i)))`

Proof

Definitions occuring in Statement :  nat-inf-infinity: `∞` nat-inf: `ℕ∞` nat: `ℕ` assert: `↑b` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` apply: `f a` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` all: `∀x:A. B[x]` assert: `↑b` ifthenelse: `if b then t else f fi ` nat-inf-infinity: `∞` btrue: `tt` true: `True` prop: `ℙ` nat-inf: `ℕ∞` implies: `P `` Q` nat: `ℕ` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]` guard: `{T}`
Lemmas referenced :  assert_wf nat_wf assert_witness equal-wf-T-base nat-inf_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 iff_imp_equal_bool nat-inf-infinity_wf all_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut independent_pairFormation lambdaFormation hypothesis thin natural_numberEquality hyp_replacement equalitySymmetry Error :applyLambdaEquality,  extract_by_obid sqequalHypSubstitution isectElimination applyEquality setElimination rename hypothesisEquality sqequalRule lambdaEquality dependent_functionElimination independent_functionElimination because_Cache baseClosed dependent_set_memberEquality addEquality unionElimination independent_isectElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll functionExtensionality functionEquality productElimination independent_pairEquality equalityTransitivity axiomEquality

Latex:
\mforall{}[x:\mBbbN{}\minfty{}].  uiff(x  =  \minfty{};\mforall{}i:\mBbbN{}.  (\muparrow{}(x  i)))

Date html generated: 2016_10_25-AM-10_14_14
Last ObjectModification: 2016_07_12-AM-06_25_05

Theory : basic

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