Nuprl Lemma : subtract_nat_wf

`∀[i,j:ℤ].  i - j ∈ ℕ supposing j ≤ i`

Proof

Definitions occuring in Statement :  nat: `ℕ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` le: `A ≤ B` member: `t ∈ T` subtract: `n - m` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` subtract: `n - m` prop: `ℙ` all: `∀x:A. B[x]` subtype_rel: `A ⊆r B` top: `Top` uiff: `uiff(P;Q)` nat_plus: `ℕ+` 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 Error :isect_memberFormation_alt,  introduction cut Error :dependent_set_memberEquality_alt,  extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis productElimination sqequalRule Error :universeIsType,  natural_numberEquality axiomEquality equalityTransitivity equalitySymmetry Error :isect_memberEquality_alt,  because_Cache Error :inhabitedIsType,  multiplyEquality independent_isectElimination dependent_functionElimination applyEquality Error :lambdaEquality_alt,  voidElimination addEquality minusEquality independent_pairFormation imageMemberEquality baseClosed independent_functionElimination unionElimination

Latex:
\mforall{}[i,j:\mBbbZ{}].    i  -  j  \mmember{}  \mBbbN{}  supposing  j  \mleq{}  i

Date html generated: 2019_06_20-AM-11_26_25
Last ObjectModification: 2018_10_03-AM-10_13_23

Theory : arithmetic

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