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Proof step 19 from proof short-law-righthift-not (previous step)

~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))))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
⊦ ( i = 32768 ∧ j = 1 → i2s(16384) ≠ i2s (bits2int ( true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false '))) ∧ ( 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, true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false '), false ' + fillsgn (32, true ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ' + false ')))))

Rule argument

Additional information

Used simplifier rules: ⊦ bits + [] = bits;% ⊦ sublist(0, 0, bits) = [];%n ≠ 0 ⊦ sublist(0, (* n), boolvar ' + bits) = boolvar ' + sublist(0, n -1, bits);% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ sgn(true ' + false ' + bits) = true ' + false ' + bits;% ⊦ sgn(boolvar ' + boolvar ' + bits) = sgn(boolvar ' + bits);% ⊦ (bits + false ')+1 = bits + true;% ⊦ (bits + true ')+1 = bits +1 + false;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ bitsinvert(false ') = true ';% ⊦ bitsinvert(true ' + bits) = false + bitsinvert(bits);% ⊦ bitsinvert(false ' + bits) = true + bitsinvert(bits);% ⊦ bits + boolvar = bits + boolvar ';% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ uint2bits(1) = false + true;%1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);