Nuprl Lemma : qminus-qsub
∀[r,s:ℚ]. (-(s - r) = (r - s) ∈ ℚ)
Proof
Definitions occuring in Statement :
qsub: r - s,
qmul: r * s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
minus: -n,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
true: True,
qsub: r - s,
squash: ↓T,
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
rationals_wf,
int-subtype-rationals,
qmul_wf,
qadd_wf,
equal_wf,
squash_wf,
true_wf,
qmul_over_plus_qrng,
qinv_inv_q,
qadd_comm_q,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
because_Cache,
minusEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
productElimination,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[r,s:\mBbbQ{}]. (-(s - r) = (r - s))
Date html generated:
2018_05_21-PM-11_51_51
Last ObjectModification:
2017_07_26-PM-06_44_43
Theory : rationals
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