Nuprl Lemma : int-rmul_functionality
∀[k1,k2:ℤ]. ∀[a,b:ℝ]. (k1 * a = k2 * b) supposing ((k1 = k2 ∈ ℤ) and (a = b))
Proof
Definitions occuring in Statement :
int-rmul: k1 * a,
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
squash: ↓T
Lemmas referenced :
req_functionality,
int-rmul_wf,
rmul_wf,
int-to-real_wf,
int-rmul-req,
req_witness,
equal-wf-base,
int_subtype_base,
req_wf,
real_wf,
req_weakening,
rmul_functionality,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
productElimination,
independent_functionElimination,
intEquality,
applyEquality,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[k1,k2:\mBbbZ{}]. \mforall{}[a,b:\mBbbR{}]. (k1 * a = k2 * b) supposing ((k1 = k2) and (a = b))
Date html generated:
2016_10_26-AM-09_05_25
Last ObjectModification:
2016_08_26-PM-01_59_45
Theory : reals
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