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Proof step 7 from proof getsetShort-theorem (previous step)

~32768 ≤ j, j ≤ 32767, ub2i(i2b(j)) < 256, 0 ≤ ub2i(i2b(j)) ⊦ ub2i(i2b(j)) + 256 * b2i(i2b(j i>> 8)) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i ∈byte → b2i(i2b(i)) = i
Proof step 9:
¬ (j i>> 8)∈byte, ~32768 ≤ j, j ≤ 32767, ub2i(i2b(j)) < 256, 0 ≤ ub2i(i2b(j)) ⊦ ub2i(i2b(j)) + 256 * b2i(i2b(j i>> 8)) = j
Proof step 51:
(j i>> 8)∈byte, ~32768 ≤ j, j ≤ 32767, ub2i(i2b(j)) < 256, 0 ≤ ub2i(i2b(j)) ⊦ ub2i(i2b(j)) + 256 * (j i>> 8) = j

Rule argument

spec: inst: name: bib-in seq: ⊦ i ∈byte → b2i(i2b(i)) = i subst: [i] → [j i>> 8] flags: rewrite, current

Additional information

Used terms: j i>> 8