### Nuprl Lemma : imin-imax-absorption

`∀[x,y:ℤ].  (imin(x;imax(x;y)) = x ∈ ℤ)`

Proof

Definitions occuring in Statement :  imin: `imin(a;b)` imax: `imax(a;b)` uall: `∀[x:A]. B[x]` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` imax: `imax(a;b)` imin: `imin(a;b)` uimplies: `b supposing a` has-value: `(a)↓` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A`
Lemmas referenced :  value-type-has-value int-value-type le_int_wf bool_wf eqtt_to_assert assert_of_le_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut hypothesis intEquality sqequalRule sqequalHypSubstitution isect_memberEquality isectElimination thin hypothesisEquality axiomEquality because_Cache extract_by_obid independent_isectElimination callbyvalueReduce lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination

Latex:
\mforall{}[x,y:\mBbbZ{}].    (imin(x;imax(x;y))  =  x)

Date html generated: 2017_04_14-AM-09_14_31
Last ObjectModification: 2017_02_27-PM-03_51_54

Theory : int_2

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