### Nuprl Lemma : not-ge-2

`∀x,y:ℤ.  uiff(¬(x ≥ y );(x + 1) ≤ y)`

Proof

Definitions occuring in Statement :  uiff: `uiff(P;Q)` ge: `i ≥ j ` le: `A ≤ B` all: `∀x:A. B[x]` not: `¬A` add: `n + m` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  all: `∀x:A. B[x]` ge: `i ≥ j ` member: `t ∈ T` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` le: `A ≤ B` not: `¬A` implies: `P `` Q` false: `False` uall: `∀[x:A]. B[x]` prop: `ℙ` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  less_than'_wf le_wf iff_weakening_uiff not_wf not-le-2 uiff_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation intEquality cut independent_pairFormation isect_memberFormation introduction hypothesis sqequalRule sqequalHypSubstitution productElimination thin independent_pairEquality lambdaEquality dependent_functionElimination hypothesisEquality voidElimination lemma_by_obid isectElimination addEquality natural_numberEquality axiomEquality equalityTransitivity equalitySymmetry because_Cache addLevel independent_isectElimination independent_functionElimination cumulativity

Latex:
\mforall{}x,y:\mBbbZ{}.    uiff(\mneg{}(x  \mgeq{}  y  );(x  +  1)  \mleq{}  y)

Date html generated: 2016_05_13-PM-03_31_03
Last ObjectModification: 2015_12_26-AM-09_46_15

Theory : arithmetic

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