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Proof step 6 from proof getShort-isi (previous step)

⊦ s2i(i2s(bor(bits2int(int2bits(b2i(byi)) + mklist(false, i→n(band(8, 31)))), band(b2i(byj), 255)))) = bor(bits2int(int2bits(b2i(byi)) + mklist(false, i→n(band(8, 31)))), band(b2i(byj), 255)), ¬ bor(bits2int(int2bits(b2i(byi)) + mklist(false, i→n(band(8, 31)))), band(b2i(byj), 255)) < ~32768 ∧ ¬ 32767 < bor(bits2int(int2bits(b2i(byi)) + mklist(false, i→n(band(8, 31)))), band(b2i(byj), 255))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ band(i, j) = bits2int(bitsand(int2bits(i), int2bits(j)))
Proof step 8:
⊦ s2i(i2s(bor(bits2int(int2bits(b2i(byi)) + mklist(false, i→n(bits2int(bitsand(int2bits(8), int2bits(31)))))), band(b2i(byj), 255)))) = bor(bits2int(int2bits(b2i(byi)) + mklist(false, i→n(bits2int(bitsand(int2bits(8), int2bits(31)))))), band(b2i(byj), 255)), ¬ bor(bits2int(int2bits(b2i(byi)) + mklist(false, i→n(bits2int(bitsand(int2bits(8), int2bits(31)))))), band(b2i(byj), 255)) < ~32768 ∧ ¬ 32767 < bor(bits2int(int2bits(b2i(byi)) + mklist(false, i→n(bits2int(bitsand(int2bits(8), int2bits(31)))))), band(b2i(byj), 255))

Rule argument

seq: ⊦ band(i, j) = bits2int(bitsand(int2bits(i), int2bits(j))) subst: [j, i] → [31, 8] rotate: F spec: intops inst: name: band-def

Additional information

Used terms: 31, 8