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
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