Nuprl Lemma : rleq-iff-not-rless
∀[x,y:ℝ]. uiff(y ≤ x;¬(x < y))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rless: x < y,
real: ℝ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
rless: x < y,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
sq_exists: ∃x:A [B[x]],
real: ℝ,
all: ∀x:A. B[x],
le: A ≤ B,
iff: P ⇐⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
rleq: x ≤ y,
rnonneg: rnonneg(x),
nat_plus: ℕ+,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
decidable: Dec(P),
or: P ∨ Q
Latex:
\mforall{}[x,y:\mBbbR{}]. uiff(y \mleq{} x;\mneg{}(x < y))
Date html generated:
2020_05_20-AM-10_56_49
Last ObjectModification:
2020_01_09-PM-01_38_47
Theory : reals
Home
Index