Nuprl Lemma : le-add-cancel4

[c,t,t':ℤ].  uiff((c t) ≤ t';c ≤ 0) supposing t' ∈ ℤ


Proof




Definitions occuring in Statement :  uiff: uiff(P;Q) uimplies: supposing a uall: [x:A]. B[x] le: A ≤ B add: m natural_number: $n int: equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a prop: uiff: uiff(P;Q) and: P ∧ Q le: A ≤ B not: ¬A implies:  Q false: False
Lemmas referenced :  le-add-cancel3 less_than'_wf le_wf equal_wf zero-add
Rules used in proof :  cut lemma_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination thin hypothesisEquality natural_numberEquality independent_isectElimination hypothesis addEquality intEquality because_Cache isect_memberFormation introduction sqequalRule productElimination independent_pairEquality isect_memberEquality lambdaEquality dependent_functionElimination axiomEquality equalityTransitivity equalitySymmetry voidElimination

Latex:
\mforall{}[c,t,t':\mBbbZ{}].    uiff((c  +  t)  \mleq{}  t';c  \mleq{}  0)  supposing  t  =  t'



Date html generated: 2016_05_13-PM-03_31_22
Last ObjectModification: 2015_12_26-AM-09_46_03

Theory : arithmetic


Home Index