Nuprl Lemma : quadratic1_functionality
∀[a,b,c,a',b',c':ℝ].
(quadratic1(a;b;c) = quadratic1(a';b';c')) supposing
((c = c') and
(b = b') and
(a = a') and
(r0 ≤ ((b * b) - r(4) * a * c)) and
a ≠ r0)
Proof
Definitions occuring in Statement :
quadratic1: quadratic1(a;b;c),
rneq: x ≠ y,
rleq: x ≤ y,
rsub: x - y,
req: x = y,
rmul: 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],
uimplies: b supposing a,
quadratic1: quadratic1(a;b;c),
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
so_apply: x[s],
false: False,
not: ¬A,
rat_term_to_real: rat_term_to_real(f;t),
rtermVar: rtermVar(var),
rat_term_ind: rat_term_ind,
pi1: fst(t),
rtermDivide: num "/" denom,
rtermMultiply: left "*" right,
rtermConstant: "const",
pi2: snd(t),
stable: Stable{P},
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
sq_type: SQType(T),
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x]
Latex:
\mforall{}[a,b,c,a',b',c':\mBbbR{}].
(quadratic1(a;b;c) = quadratic1(a';b';c')) supposing
((c = c') and
(b = b') and
(a = a') and
(r0 \mleq{} ((b * b) - r(4) * a * c)) and
a \mneq{} r0)
Date html generated:
2020_05_20-PM-00_33_21
Last ObjectModification:
2020_01_06-PM-00_14_02
Theory : reals
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