Nuprl Lemma : test-q-norm-conv
∀[a,b,c:ℚ]. (((a + b) * (c + b)) = (((a * c) + (b * c)) + (b * b) + (a * b)) ∈ ℚ)
Proof
Definitions occuring in Statement :
qmul: r * s,
qadd: r + s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
true: True,
squash: ↓T,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
rationals_wf,
qadd_wf,
qmul_wf,
equal_wf,
squash_wf,
true_wf,
qmul_over_plus_qrng,
mon_assoc_q,
qadd_ac_1_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,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
productElimination,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[a,b,c:\mBbbQ{}]. (((a + b) * (c + b)) = (((a * c) + (b * c)) + (b * b) + (a * b)))
Date html generated:
2018_05_21-PM-11_51_21
Last ObjectModification:
2017_07_26-PM-06_44_28
Theory : rationals
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