Nuprl Lemma : r2-det-convex3
∀[p,q,r,t,s:ℝ^2]. ∀[a,b,c:ℝ].
|a*p + b*q + c*rts| = ((a * |pts|) + (b * |qts|) + (c * |rts|)) supposing (a + b + c) = r1
Proof
Definitions occuring in Statement :
r2-det: |pqr|,
real-vec-mul: a*X,
real-vec-add: X + Y,
real-vec: ℝ^n,
req: x = y,
rmul: a * b,
radd: a + b,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q,
false: False,
stable: Stable{P},
prop: ℙ,
or: P ∨ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
all: ∀x:A. B[x],
req_int_terms: t1 ≡ t2,
req-vec: req-vec(n;x;y),
real-vec-mul: a*X,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x]
Latex:
\mforall{}[p,q,r,t,s:\mBbbR{}\^{}2]. \mforall{}[a,b,c:\mBbbR{}].
|a*p + b*q + c*rts| = ((a * |pts|) + (b * |qts|) + (c * |rts|)) supposing (a + b + c) = r1
Date html generated:
2020_05_20-PM-00_59_38
Last ObjectModification:
2020_01_02-AM-11_48_21
Theory : reals
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