### Nuprl Lemma : subtract-is-int-iff

`∀[a,b:Base].  uiff(a - b ∈ ℤ;(a ∈ ℤ) ∧ (b ∈ ℤ))`

Proof

Definitions occuring in Statement :  uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` and: `P ∧ Q` member: `t ∈ T` subtract: `n - m` int: `ℤ` base: `Base`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` subtract: `n - m` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` prop: `ℙ` implies: `P `` Q` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  minus-is-int-iff add-is-int-iff iff_weakening_uiff iff_transitivity uiff_wf base_wf equal-wf-base
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution productElimination thin independent_pairEquality isect_memberEquality isectElimination hypothesisEquality axiomEquality equalityTransitivity hypothesis equalitySymmetry lemma_by_obid intEquality baseApply closedConclusion baseClosed because_Cache productEquality independent_pairFormation instantiate cumulativity addLevel independent_isectElimination independent_functionElimination lambdaFormation

Latex:
\mforall{}[a,b:Base].    uiff(a  -  b  \mmember{}  \mBbbZ{};(a  \mmember{}  \mBbbZ{})  \mwedge{}  (b  \mmember{}  \mBbbZ{}))

Date html generated: 2016_05_13-PM-03_28_37
Last ObjectModification: 2016_01_14-PM-06_42_07

Theory : arithmetic

Home Index