Nuprl Lemma : square-is-zero
∀x:ℝ. ((x * x) = r0 ⇐⇒ x = r0)
Proof
Definitions occuring in Statement :
req: x = y,
rmul: a * b,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
rev_implies: P ⇐ Q,
guard: {T},
uimplies: b supposing a,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
false: False,
uiff: uiff(P;Q),
squash: ↓T,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
true: True,
subtype_rel: A ⊆r B,
rneq: x ≠ y,
rless: x < y,
sq_exists: ∃x:A [B[x]],
less_than: a < b
Latex:
\mforall{}x:\mBbbR{}. ((x * x) = r0 \mLeftarrow{}{}\mRightarrow{} x = r0)
Date html generated:
2020_05_20-AM-11_08_10
Last ObjectModification:
2019_12_14-PM-00_56_01
Theory : reals
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