Nuprl Lemma : qsub_wf
∀[r,s:ℚ]. (r - s ∈ ℚ)
Proof
Definitions occuring in Statement :
qsub: r - s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
qsub: r - s,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
qadd_wf,
qmul_wf,
int-subtype-rationals,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
minusEquality,
natural_numberEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[r,s:\mBbbQ{}]. (r - s \mmember{} \mBbbQ{})
Date html generated:
2016_05_15-PM-10_39_27
Last ObjectModification:
2015_12_27-PM-07_59_16
Theory : rationals
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