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Proof step 6 from proof fits-law-band (previous step)

8 < # int2bits(band(b2i(by1), b2i(by2))) ⊦ band(b2i(by1), b2i(by2)) = cast(8, band(b2i(by1), b2i(by2)))

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 7:
# int2bits(i) < n, # int2bits(j) < n ⊦ # int2bits(band(i, j)) < n
Proof step 8:
8 < # int2bits(band(b2i(by1), b2i(by2))) ⊦ # int2bits(b2i(by1)) < 9 ∧ # int2bits(b2i(by2)) < 9, band(b2i(by1), b2i(by2)) = cast(8, band(b2i(by1), b2i(by2)))

Rule argument

seq: # int2bits(i) < n, # int2bits(j) < n ⊦ # int2bits(band(i, j)) < n subst: [i, n, j] → [b2i(by1), 9, b2i(by2)] rotate: F spec: intops inst: name: band-bitlength

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ m < n → n ≠ 0; (forward) Used terms: b2i(by1), 9, b2i(by2)