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Proof step 5 from proof fits-law-shr-01 (previous step)

abs(s2i(sho) i>> band(i, 31)) ≤ abs(s2i(sho)) ⊦ s2i(sho) i>> band(i, 31) = s2i(i2s(s2i(sho) i>> band(i, 31)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i ≤ 0 ∧ j ≤ 0 → (abs(i) ≤ abs(j) ↔ j ≤ i)
Proof step 7:
¬(s2i(sho) i>> band(i, 31) ≤ 0 ∧ s2i(sho) ≤ 0), abs(s2i(sho) i>> band(i, 31)) ≤ abs(s2i(sho)) ⊦ s2i(sho) i>> band(i, 31) = s2i(i2s(s2i(sho) i>> band(i, 31)))
Proof step 21:
s2i(sho) i>> band(i, 31) ≤ 0 ∧ s2i(sho) ≤ 0, s2i(sho) ≤ s2i(sho) i>> band(i, 31) ⊦ s2i(sho) i>> band(i, 31) = s2i(i2s(s2i(sho) i>> band(i, 31)))

Rule argument

seq: ⊦ i ≤ 0 ∧ j ≤ 0 → (abs(i) ≤ abs(j) ↔ j ≤ i) subst: [j, i] → [s2i(sho), s2i(sho) i>> band(i, 31)] rotate: F spec: int-abs inst: name: absle-01

Additional information

Used terms: s2i(sho), s2i(sho) i>> band(i, 31)