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Proof step 17 from proof short-law-righthift-not (previous step)

⊦ (i = 32768 ∧ j = 1 → i2s(16384) ≠ i2s((# int2bits(~32768) ≤ 1 ⊃ ~1;bits2int(sublist(0, # int2bits(~32768) - 1, int2bits(~32768)))))) ∧ ( i = 32768 ∧ j = 1 → i2s (bits2int (sublist (0, # fillsgn (32, ( ( ( ( ( ( (((((((((false ' + true ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false '), false ' + fillsgn (32, ( ( ( ( ( ( (((((((((false ' + true ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ')))) ≠ i2s(bits2int(sublist(0, # fillsgn(32, int2bits(~32768)), false ' + fillsgn(32, int2bits(~32768))))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
i < 0 ⊦ int2bits((* i)) = sgn(bitsinvert(uint2bits(abs(i))) +1)
Proof step 19:
~32768 < 0 ⊦ ( i = 32768 ∧ j = 1 → i2s(16384) ≠ i2s ((# sgn(bitsinvert(uint2bits(abs(~32768))) +1) ≤ 1 ⊃ ~1 ;bits2int(sublist(0, # sgn(bitsinvert(uint2bits(abs(~32768))) +1) - 1, sgn(bitsinvert(uint2bits(abs(~32768))) +1))) ))) ∧ ( i = 32768 ∧ j = 1 → i2s (bits2int (sublist (0, # fillsgn (32, ( ( ( ( ( ( (((((((((false ' + true ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false '), false ' + fillsgn (32, ( ( ( ( ( ( (((((((((false ' + true ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ') + false ')))) ≠ i2s (bits2int (sublist(0, # fillsgn(32, sgn(bitsinvert(uint2bits(abs(~32768))) +1)), false ' + fillsgn(32, sgn(bitsinvert(uint2bits(abs(~32768))) +1))))))

Rule argument

seq: i < 0 ⊦ int2bits((* i)) = sgn(bitsinvert(uint2bits(abs(i))) +1) subst: [i] → [~32768] rotate: F spec: int2bits inst: name: int2bits-neg-num

Additional information

Used terms: ~32768