### Nuprl Lemma : ndiff_ndiff

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

Proof

Definitions occuring in Statement :  ndiff: `a -- b` nat: `ℕ` uall: `∀[x:A]. B[x]` add: `n + m` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  ndiff: `a -- b` imax: `imax(a;b)` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing 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 ` nat: `ℕ` 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` le: `A ≤ B` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` squash: `↓T` subtract: `n - m` subtype_rel: `A ⊆r B` true: `True` 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 nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermSubtract_wf itermConstant_wf itermVar_wf intformnot_wf itermAdd_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_subtract_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_not_lemma int_term_value_add_lemma int_formula_prop_wf ifthenelse_wf squash_wf true_wf add-associates minus-one-mul minus-add minus-one-mul-top
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 natural_numberEquality lambdaFormation unionElimination equalityElimination productElimination setElimination rename dependent_pairFormation equalityTransitivity equalitySymmetry promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination addEquality lambdaEquality int_eqEquality voidEquality independent_pairFormation computeAll applyEquality imageElimination universeEquality minusEquality imageMemberEquality baseClosed callbyvalueReduce

Latex:
\mforall{}[a,b:\mBbbZ{}].  \mforall{}[c:\mBbbN{}].    (((a  --  b)  --  c)  =  (a  --  (b  +  c)))

Date html generated: 2017_04_14-AM-09_14_58
Last ObjectModification: 2017_02_27-PM-03_52_56

Theory : int_2

Home Index