`∀[L1,L2:ℝ List].  radd-list(L1) ≤ radd-list(L2) supposing (||L1|| = ||L2|| ∈ ℤ) ∧ (∀i:ℕ||L1||. (L1[i] ≤ L2[i]))`

Proof

Definitions occuring in Statement :  rleq: `x ≤ y` radd-list: `radd-list(L)` real: `ℝ` select: `L[n]` length: `||as||` list: `T List` int_seg: `{i..j-}` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` and: `P ∧ Q` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` uimplies: `b supposing a` and: `P ∧ Q` prop: `ℙ` int_seg: `{i..j-}` guard: `{T}` lelt: `i ≤ j < k` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` so_apply: `x[s]` subtype_rel: `A ⊆r B` select: `L[n]` nil: `[]` it: `⋅` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` rleq: `x ≤ y` rnonneg: `rnonneg(x)` le: `A ≤ B` real: `ℝ` ge: `i ≥ j ` uiff: `uiff(P;Q)` rev_uimplies: `rev_uimplies(P;Q)` cand: `A c∧ B` subtract: `n - m` less_than: `a < b` true: `True` squash: `↓T` sq_type: `SQType(T)` iff: `P `⇐⇒` Q` rge: `x ≥ y` less_than': `less_than'(a;b)` nat_plus: `ℕ+` cons: `[a / b]`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin extract_by_obid sqequalHypSubstitution isectElimination hypothesis sqequalRule lambdaEquality productEquality intEquality because_Cache hypothesisEquality natural_numberEquality setElimination rename independent_isectElimination equalityTransitivity equalitySymmetry productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll applyEquality independent_functionElimination baseClosed lambdaFormation independent_pairEquality minusEquality axiomEquality pointwiseFunctionality promote_hyp baseApply closedConclusion addEquality dependent_set_memberEquality hyp_replacement imageElimination cumulativity universeEquality imageMemberEquality instantiate applyLambdaEquality

Latex:
\mforall{}[L1,L2:\mBbbR{}  List].
radd-list(L1)  \mleq{}  radd-list(L2)  supposing  (||L1||  =  ||L2||)  \mwedge{}  (\mforall{}i:\mBbbN{}||L1||.  (L1[i]  \mleq{}  L2[i]))

Date html generated: 2017_10_03-AM-08_26_13
Last ObjectModification: 2017_07_28-AM-07_24_12

Theory : reals

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