Nuprl Lemma : subtract-is-less
∀[x,y:ℤ]. uiff(x - y < x;0 < y)
Proof
Definitions occuring in Statement :
less_than: a < b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
top: Top,
subtract: n - m,
subtype_rel: A ⊆r B
Lemmas referenced :
less_than_wf,
subtract_wf,
member-less_than,
add_functionality_wrt_lt,
le_reflexive,
add-associates,
minus-one-mul,
add-swap,
add-mul-special,
add-commutes,
zero-mul,
zero-add,
minus-one-mul-top,
add-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
sqequalRule,
productElimination,
independent_pairEquality,
isect_memberEquality,
independent_isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
multiplyEquality,
minusEquality,
addEquality,
applyEquality,
lambdaEquality
Latex:
\mforall{}[x,y:\mBbbZ{}]. uiff(x - y < x;0 < y)
Date html generated:
2016_05_13-PM-03_31_38
Last ObjectModification:
2015_12_26-AM-09_45_49
Theory : arithmetic
Home
Index