Nuprl Lemma : imin_lb

a,b,c:ℤ.  (imin(a;b) ≤ ⇐⇒ (a ≤ c) ∨ (b ≤ c))


Proof




Definitions occuring in Statement :  imin: imin(a;b) le: A ≤ B all: x:A. B[x] iff: ⇐⇒ Q or: P ∨ Q int:
Definitions unfolded in proof :  imin: imin(a;b) all: x:A. B[x] has-value: (a)↓ uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a implies:  Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) and: P ∧ Q ifthenelse: if then else fi  iff: ⇐⇒ Q or: P ∨ Q decidable: Dec(P) satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False not: ¬A top: Top prop: rev_implies:  Q bfalse: ff sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b
Lemmas referenced :  value-type-has-value int-value-type le_int_wf bool_wf eqtt_to_assert assert_of_le_int decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_wf le_wf or_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation callbyvalueReduce cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin intEquality independent_isectElimination hypothesis hypothesisEquality because_Cache unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_pairFormation inlFormation dependent_functionElimination natural_numberEquality dependent_pairFormation lambdaEquality int_eqEquality isect_memberEquality voidElimination voidEquality computeAll promote_hyp instantiate cumulativity independent_functionElimination inrFormation

Latex:
\mforall{}a,b,c:\mBbbZ{}.    (imin(a;b)  \mleq{}  c  \mLeftarrow{}{}\mRightarrow{}  (a  \mleq{}  c)  \mvee{}  (b  \mleq{}  c))



Date html generated: 2017_04_14-AM-09_14_45
Last ObjectModification: 2017_02_27-PM-03_52_51

Theory : int_2


Home Index