### Nuprl Lemma : int_loset_wf

`int_loset() ∈ LOSet`

Proof

Definitions occuring in Statement :  int_loset: `int_loset()` loset: `LOSet` member: `t ∈ T`
Definitions unfolded in proof :  int_loset: `int_loset()` member: `t ∈ T` uall: `∀[x:A]. B[x]` uimplies: `b supposing a` eqfun_p: `IsEqFun(T;eq)` infix_ap: `x f y` uiff: `uiff(P;Q)` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` implies: `P `` Q` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` le: `A ≤ B` not: `¬A` false: `False` ulinorder: `UniformLinorder(T;x,y.R[x; y])` uorder: `UniformOrder(T;x,y.R[x; y])` urefl: `UniformlyRefl(T;x,y.E[x; y])` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` utrans: `UniformlyTrans(T;x,y.E[x; y])` uanti_sym: `UniformlyAntiSym(T;x,y.R[x; y])` connex: `Connex(T;x,y.R[x; y])`
Lemmas referenced :  mk_oset_wf eq_int_wf le_int_wf equal-wf-base int_subtype_base iff_weakening_uiff assert_wf assert_of_eq_int assert_witness uall_wf uiff_wf ulinorder_functionality_wrt_iff le_wf assert_of_le_int less_than'_wf decidable__le satisfiable-full-omega-tt intformnot_wf intformle_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_wf intformand_wf int_formula_prop_and_lemma decidable__equal_int intformeq_wf int_formula_prop_eq_lemma decidable__or intformor_wf int_formula_prop_or_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin intEquality lambdaEquality hypothesisEquality hypothesis independent_isectElimination sqequalRule isect_memberFormation independent_pairFormation applyEquality because_Cache productElimination independent_pairEquality isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry addLevel uallFunctionality independent_functionElimination cumulativity instantiate dependent_functionElimination voidElimination unionElimination natural_numberEquality dependent_pairFormation int_eqEquality voidEquality computeAll lambdaFormation

Latex:
int\_loset()  \mmember{}  LOSet

Date html generated: 2017_10_01-AM-08_13_23
Last ObjectModification: 2017_02_28-PM-01_57_59

Theory : sets_1

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