### Nuprl Lemma : imax-wf-partial-nat

`∀[x,y:partial(ℕ)].  (imax(x;y) ∈ partial(ℕ))`

Proof

Definitions occuring in Statement :  partial: `partial(T)` imax: `imax(a;b)` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  guard: `{T}` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` nat: `ℕ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` and: `P ∧ Q` cand: `A c∧ B` all: `∀x:A. B[x]` implies: `P `` Q` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` top: `Top` prop: `ℙ` subtype_rel: `A ⊆r B` imax: `imax(a;b)` has-value: `(a)↓` squash: `↓T` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` rev_implies: `P `` Q` iff: `P `⇐⇒` Q`
Lemmas referenced :  partial-base subtype_rel_partial nat_wf base_wf set_subtype_base le_wf istype-int int_subtype_base subtype_rel_transitivity partial_wf set-value-type int-value-type inclusion-partial imax_wf nat_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf intformeq_wf int_formula_prop_and_lemma istype-void int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_formula_prop_wf is-exception_wf not_wf has-value_wf_base apply-2-partial termination exception-not-value le_int_wf eqtt_to_assert assert_of_le_int eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot iff_weakening_uiff assert_wf bool_wf
Rules used in proof :  cut introduction extract_by_obid hypothesis sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination thin independent_isectElimination sqequalRule intEquality Error :lambdaEquality_alt,  natural_numberEquality hypothesisEquality because_Cache independent_pairFormation baseClosed Error :dependent_set_memberEquality_alt,  setElimination rename Error :inhabitedIsType,  Error :lambdaFormation_alt,  equalityTransitivity equalitySymmetry applyLambdaEquality dependent_functionElimination unionElimination approximateComputation independent_functionElimination Error :dependent_pairFormation_alt,  int_eqEquality Error :isect_memberEquality_alt,  voidElimination Error :universeIsType,  Error :equalityIsType1,  productElimination baseApply closedConclusion applyEquality Error :productIsType,  callbyvalueCallbyvalue callbyvalueReduce callbyvalueExceptionCases imageElimination imageMemberEquality equalityElimination Error :equalityIsType2,  promote_hyp instantiate cumulativity

Latex:
\mforall{}[x,y:partial(\mBbbN{})].    (imax(x;y)  \mmember{}  partial(\mBbbN{}))

Date html generated: 2019_06_20-PM-01_13_43
Last ObjectModification: 2018_10_07-AM-00_11_31

Theory : int_2

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