Nuprl Lemma : mul_cancel_in_lt
∀[a,b:ℤ]. ∀[n:ℕ+].  a < b supposing n * a < n * b
Proof
Definitions occuring in Statement : 
nat_plus: ℕ+
, 
less_than: a < b
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
multiply: n * m
, 
int: ℤ
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
prop: ℙ
, 
nat_plus: ℕ+
, 
all: ∀x:A. B[x]
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
subtype_rel: A ⊆r B
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
gt: i > j
, 
le: A ≤ B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
false: False
, 
guard: {T}
, 
implies: P 
⇒ Q
Lemmas referenced : 
less_than_irreflexivity, 
less_than_transitivity1, 
int_subtype_base, 
set_subtype_base, 
multiply-is-int-iff, 
not-gt-2, 
nat_plus_subtype_nat, 
mul_preserves_le, 
decidable__lt, 
nat_plus_wf, 
member-less_than, 
less_than_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
hypothesis, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
multiplyEquality, 
setElimination, 
rename, 
hypothesisEquality, 
sqequalRule, 
isect_memberEquality, 
independent_isectElimination, 
because_Cache, 
equalityTransitivity, 
equalitySymmetry, 
intEquality, 
dependent_functionElimination, 
unionElimination, 
applyEquality, 
productElimination, 
baseApply, 
closedConclusion, 
baseClosed, 
lambdaEquality, 
natural_numberEquality, 
independent_functionElimination, 
voidElimination
Latex:
\mforall{}[a,b:\mBbbZ{}].  \mforall{}[n:\mBbbN{}\msupplus{}].    a  <  b  supposing  n  *  a  <  n  *  b
Date html generated:
2016_05_13-PM-03_40_48
Last ObjectModification:
2016_01_14-PM-06_38_35
Theory : arithmetic
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