Nuprl Lemma : convex-comb-0-1
∀[x,y:ℝ]. ∀[t:{t:ℝ| t ≠ r0} ]. (convex-comb(x;y;r0;t) = y)
Proof
Definitions occuring in Statement :
convex-comb: convex-comb(x;y;r;s),
rneq: x ≠ y,
req: x = y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
all: ∀x:A. B[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top,
convex-comb: convex-comb(x;y;r;s),
rat_term_to_real: rat_term_to_real(f;t),
rtermVar: rtermVar(var),
rat_term_ind: rat_term_ind,
pi1: fst(t),
true: True,
rtermDivide: num "/" denom,
rtermMultiply: left "*" right,
pi2: snd(t),
rdiv: (x/y),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
sq_stable__req,
convex-comb_wf1,
int-to-real_wf,
rneq_wf,
radd_wf,
real_wf,
itermSubtract_wf,
itermAdd_wf,
itermConstant_wf,
itermVar_wf,
sq_stable__rneq,
rneq_functionality,
req_weakening,
req-iff-rsub-is-0,
real_polynomial_null,
istype-int,
real_term_value_sub_lemma,
istype-void,
real_term_value_add_lemma,
real_term_value_const_lemma,
real_term_value_var_lemma,
rdiv_wf,
rmul_wf,
rinv_wf2,
itermMultiply_wf,
assert-rat-term-eq2,
rtermDivide_wf,
rtermMultiply_wf,
rtermVar_wf,
req_functionality,
req_transitivity,
rmul_functionality,
rinv_functionality2,
rinv-mul-as-rdiv,
real_term_value_mul_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
closedConclusion,
natural_numberEquality,
hypothesis,
setElimination,
rename,
dependent_set_memberEquality_alt,
universeIsType,
independent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
setIsType,
because_Cache,
inhabitedIsType,
dependent_functionElimination,
independent_isectElimination,
productElimination,
approximateComputation,
lambdaEquality_alt,
int_eqEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation
Latex:
\mforall{}[x,y:\mBbbR{}]. \mforall{}[t:\{t:\mBbbR{}| t \mneq{} r0\} ]. (convex-comb(x;y;r0;t) = y)
Date html generated:
2019_10_31-AM-06_25_09
Last ObjectModification:
2019_04_02-PM-10_18_37
Theory : reals_2
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