### Nuprl Lemma : ndiff_ndiff_eq_imin

`∀[a,b:ℕ].  ((a -- (a -- b)) = imin(a;b) ∈ ℤ)`

Proof

Definitions occuring in Statement :  ndiff: `a -- b` imin: `imin(a;b)` nat: `ℕ` uall: `∀[x:A]. B[x]` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  imin: `imin(a;b)` ndiff: `a -- b` imax: `imax(a;b)` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` nat: `ℕ` 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` so_lambda: `λ2x.t[x]` so_apply: `x[s]` ge: `i ≥ j ` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` has-value: `(a)↓`
Lemmas referenced :  nat_wf value-type-has-value int-value-type subtract_wf 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 set-value-type nat_properties decidable__equal_int satisfiable-full-omega-tt intformand_wf intformnot_wf intformeq_wf itermConstant_wf itermVar_wf intformle_wf itermSubtract_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_le_lemma int_term_value_subtract_lemma int_formula_prop_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut hypothesis extract_by_obid sqequalHypSubstitution isect_memberEquality isectElimination thin hypothesisEquality axiomEquality because_Cache intEquality independent_isectElimination setElimination rename natural_numberEquality lambdaFormation unionElimination equalityElimination productElimination dependent_pairFormation equalityTransitivity equalitySymmetry promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination lambdaEquality int_eqEquality voidEquality independent_pairFormation computeAll callbyvalueReduce

Latex:
\mforall{}[a,b:\mBbbN{}].    ((a  --  (a  --  b))  =  imin(a;b))

Date html generated: 2017_04_14-AM-09_15_01
Last ObjectModification: 2017_02_27-PM-03_52_58

Theory : int_2

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