Nuprl Lemma : rmul_functionality
∀[r1,r2,s1,s2:ℝ]. ((r1 * s1) = (r2 * s2)) supposing ((s1 = s2) and (r1 = r2))
Proof
Definitions occuring in Statement :
req: x = y
,
rmul: a * b
,
real: ℝ
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uimplies: b supposing a
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
all: ∀x:A. B[x]
,
subtype_rel: A ⊆r B
,
real: ℝ
,
implies: P
⇒ Q
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
prop: ℙ
Lemmas referenced :
req-iff-bdd-diff,
rmul_wf,
bdd-diff_functionality,
reg-seq-mul_wf,
rmul-bdd-diff-reg-seq-mul,
reg-seq-mul_functionality_wrt_bdd-diff,
req_witness,
req_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
dependent_functionElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
because_Cache,
sqequalRule,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[r1,r2,s1,s2:\mBbbR{}]. ((r1 * s1) = (r2 * s2)) supposing ((s1 = s2) and (r1 = r2))
Date html generated:
2016_05_18-AM-06_51_33
Last ObjectModification:
2015_12_28-AM-00_29_51
Theory : reals
Home
Index