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: uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  guard: {T} uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a nat: so_lambda: λ2x.t[x] so_apply: x[s] and: P ∧ Q cand: c∧ B all: x:A. B[x] implies:  Q ge: i ≥  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: subtype_rel: A ⊆B imax: imax(a;b) has-value: (a)↓ squash: T bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) ifthenelse: if then else fi  bfalse: ff sq_type: SQType(T) bnot: ¬bb assert: b rev_implies:  Q iff: ⇐⇒ 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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