`∀[a,b,n:ℤ].  uiff(a < b;a + n < b + n)`

Proof

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

Latex:
\mforall{}[a,b,n:\mBbbZ{}].    uiff(a  <  b;a  +  n  <  b  +  n)

Date html generated: 2016_05_13-PM-03_39_58
Last ObjectModification: 2016_01_14-PM-06_38_42

Theory : arithmetic

Home Index