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Reference · Lemmas behind operations-research checks

rainbow.math.lemmas.ista-shrink

Lemmas behind operations-research checks src/rainbow/math/lemmas/ista_shrink.clj0 definitions, 1 theorems

General lemmas: ista shrink. The mathematical facts the corresponding checks rest on, each checked by the kernel.

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signed/soft-threshold-reading

TheoremFor all inputsNo axiomsSource

signed/soft-threshold-reading :
  (st-a st-y st-m st-x st-c : ℚ)
  (st-ha : 0 ≤ st-a)
  (st-hy : st-a · st-a = st-y · st-y)
  (st-hg : st-a + signed/negate st-c ≤ st-m)
  (st-hm : 0 ≤ st-m)
  (st-hp : st-m · (st-m + signed/negate (st-a + signed/negate st-c)) = 0)
  (st-hx : st-x · st-x = st-m · st-m)
  (st-hc : 0 ≤ st-c)
  → proposition/conjunction (conjunction) (conjunction₁)
  where conjunction := proposition/conjunction (proposition/disjunction (st-m = 0) (st-m = st-a + signed/negate st-c)) (proposition/conjunction (0 ≤ st-m) (st-a + signed/negate st-c ≤ st-m))
  where conjunction₁ := proposition/conjunction (st-m ≤ st-a) (proposition/conjunction (st-x · st-x ≤ st-y · st-y) (∀ (st-z : st-a ≤ st-c), st-x = 0))

+ = signed/add0 = signed/zero= = signed/equivalent: equality of rational values· = signed/multiplyℚ = signed/SignedRational≤ = signed/at-most