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Proof step 2 from proof short-law-righthift-not (previous step)

⊦ ( i = 32768 ∧ j = 1 → i2s ((# int2bits(32768) ≤ i→n(bits2int(bitsand(int2bits(1), int2bits(31)))) ⊃ 0 ;bits2int(sublist(0, # int2bits(32768) - i→n(bits2int(bitsand(int2bits(1), int2bits(31)))), int2bits(32768))) )) ≠ i2s ((# int2bits(~32768) ≤ i→n(bits2int(bitsand(int2bits(1), int2bits(31)))) ⊃ ~1 ;bits2int(sublist(0, # int2bits(~32768) - i→n(bits2int(bitsand(int2bits(1), int2bits(31)))), int2bits(~32768))) ))) ∧ (i = 32768 ∧ j = 1 → i2s(32768 i>>> 1) ≠ i2s(~32768 i>>> 1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i i>>> j = bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i))))
Proof step 4:
⊦ ( i = 32768 ∧ j = 1 → i2s ((# int2bits(32768) ≤ i→n(bits2int(bitsand(int2bits(1), int2bits(31)))) ⊃ 0 ;bits2int(sublist(0, # int2bits(32768) - i→n(bits2int(bitsand(int2bits(1), int2bits(31)))), int2bits(32768))) )) ≠ i2s ((# int2bits(~32768) ≤ i→n(bits2int(bitsand(int2bits(1), int2bits(31)))) ⊃ ~1 ;bits2int(sublist(0, # int2bits(~32768) - i→n(bits2int(bitsand(int2bits(1), int2bits(31)))), int2bits(~32768))) ))) ∧ ( i = 32768 ∧ j = 1 → i2s(32768 i>>> 1) ≠ i2s(bits2int(sublist(0, # fillsgn(32, int2bits(~32768)), mklist(false, i→n(band(1, 31))) + fillsgn(32, int2bits(~32768))))))

Rule argument

seq: ⊦ i i>>> j = bits2int (sublist (0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) subst: [j, i] → [1, ~32768] rotate: F spec: intops inst: name: shiftrzero-def

Additional information

Used terms: 1, ~32768