### Nuprl Lemma : reg-seq-mul-assoc

`∀x,y,z:ℝ.  bdd-diff(reg-seq-mul(reg-seq-mul(x;y);z);reg-seq-mul(x;reg-seq-mul(y;z)))`

Proof

Definitions occuring in Statement :  reg-seq-mul: `reg-seq-mul(x;y)` real: `ℝ` bdd-diff: `bdd-diff(f;g)` all: `∀x:A. B[x]`
Definitions unfolded in proof :  all: `∀x:A. B[x]` reg-seq-mul: `reg-seq-mul(x;y)` bdd-diff: `bdd-diff(f;g)` exists: `∃x:A. B[x]` member: `t ∈ T` nat: `ℕ` uall: `∀[x:A]. B[x]` subtype_rel: `A ⊆r B` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` int_upper: `{i...}` so_lambda: `λ2x.t[x]` real: `ℝ` nat_plus: `ℕ+` so_apply: `x[s]` uimplies: `b supposing a` guard: `{T}` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` uiff: `uiff(P;Q)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` nequal: `a ≠ b ∈ T ` squash: `↓T` true: `True` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` int_nzero: `ℤ-o` sq_stable: `SqStable(P)` rev_uimplies: `rev_uimplies(P;Q)` subtract: `n - m` sq_type: `SQType(T)` less_than: `a < b` cand: `A c∧ B`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation sqequalRule dependent_pairFormation dependent_set_memberEquality addEquality multiplyEquality natural_numberEquality cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis applyEquality because_Cache independent_pairFormation lambdaEquality setElimination rename setEquality independent_isectElimination equalityTransitivity equalitySymmetry applyLambdaEquality dependent_functionElimination unionElimination pointwiseFunctionality promote_hyp baseApply closedConclusion baseClosed productElimination int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll independent_functionElimination divideEquality imageElimination imageMemberEquality universeEquality remainderEquality minusEquality instantiate cumulativity inlFormation inrFormation

Latex:
\mforall{}x,y,z:\mBbbR{}.    bdd-diff(reg-seq-mul(reg-seq-mul(x;y);z);reg-seq-mul(x;reg-seq-mul(y;z)))

Date html generated: 2017_10_02-PM-07_14_56
Last ObjectModification: 2017_07_28-AM-07_20_17

Theory : reals

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