`∀x,y:ℤ.  (0 ≤ (x + y)) supposing ((0 ≤ x) and (0 ≤ y))`

Proof

Definitions occuring in Statement :  uimplies: `b supposing a` le: `A ≤ B` all: `∀x:A. B[x]` add: `n + m` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uimplies: `b supposing a` member: `t ∈ T` decidable: `Dec(P)` or: `P ∨ Q` uall: `∀[x:A]. B[x]` sq_type: `SQType(T)` implies: `P `` Q` guard: `{T}` prop: `ℙ` not: `¬A` false: `False` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` le: `A ≤ B`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut isect_memberFormation lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin because_Cache hypothesis unionElimination instantiate isectElimination cumulativity intEquality independent_isectElimination independent_functionElimination hypothesisEquality sqequalRule inrFormation natural_numberEquality addEquality inlFormation voidElimination addLevel introduction productElimination independent_pairEquality lambdaEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality isectEquality

Latex:
\mforall{}x,y:\mBbbZ{}.    (0  \mleq{}  (x  +  y))  supposing  ((0  \mleq{}  x)  and  (0  \mleq{}  y))

Date html generated: 2016_05_13-PM-03_30_32
Last ObjectModification: 2015_12_26-AM-09_46_51

Theory : arithmetic

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