`∀[i:ℕ]. ∀[j:ℕ+].  (i + j ∈ ℕ+)`

Proof

Definitions occuring in Statement :  nat_plus: `ℕ+` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` add: `n + m`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat_plus: `ℕ+` nat: `ℕ` prop: `ℙ` all: `∀x:A. B[x]` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` top: `Top` subtract: `n - m` ge: `i ≥ j ` subtype_rel: `A ⊆r B` le: `A ≤ B` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` true: `True` implies: `P `` Q` not: `¬A` false: `False` decidable: `Dec(P)` or: `P ∨ Q`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut dependent_set_memberEquality addEquality sqequalHypSubstitution setElimination thin rename hypothesisEquality lemma_by_obid isectElimination natural_numberEquality hypothesis sqequalRule axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache dependent_functionElimination productElimination independent_isectElimination multiplyEquality voidElimination voidEquality minusEquality applyEquality lambdaEquality intEquality independent_pairFormation imageMemberEquality baseClosed independent_functionElimination unionElimination

Latex:
\mforall{}[i:\mBbbN{}].  \mforall{}[j:\mBbbN{}\msupplus{}].    (i  +  j  \mmember{}  \mBbbN{}\msupplus{})

Date html generated: 2016_05_13-PM-03_39_23
Last ObjectModification: 2016_01_14-PM-06_38_31

Theory : arithmetic

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