Nuprl Lemma : qsub-sub
∀[a,b:ℤ]. (a - b ~ a - b)
Proof
Definitions occuring in Statement :
qsub: r - s,
uall: ∀[x:A]. B[x],
subtract: n - m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
qsub: r - s,
subtract: n - m,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
qadd-add,
qmul-mul,
qminus-minus
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
sqequalRule,
hypothesisEquality,
minusEquality,
natural_numberEquality,
multiplyEquality,
addEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
intEquality,
isect_memberEquality
Latex:
\mforall{}[a,b:\mBbbZ{}]. (a - b \msim{} a - b)
Date html generated:
2016_05_15-PM-10_45_02
Last ObjectModification:
2015_12_27-PM-07_54_00
Theory : rationals
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