Nuprl Lemma : qmul-qdiv-cancel3
∀[a,b,c:ℚ]. (a * (b/a) * c) = (b * c) ∈ ℚ supposing ¬(a = 0 ∈ ℚ)
Proof
Definitions occuring in Statement :
qdiv: (r/s),
qmul: r * s,
rationals: ℚ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
qmul_assoc_qrng,
qdiv_wf,
qmul_wf,
iff_weakening_equal,
rationals_wf,
qmul-qdiv-cancel,
not_wf,
equal-wf-T-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
because_Cache,
independent_isectElimination,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[a,b,c:\mBbbQ{}]. (a * (b/a) * c) = (b * c) supposing \mneg{}(a = 0)
Date html generated:
2018_05_21-PM-11_50_56
Last ObjectModification:
2017_07_26-PM-06_44_13
Theory : rationals
Home
Index