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Proof step 2 from proof int2bits-mod2 (previous step)

j < 0 ⊦ fillsgn(2, int2bits(j % 2)).rest = int2bits(j % 2)

User applied rule cut formula

And closed the goal!

Rule argument

fma: j % 2 = ~1

Additional information

Used simplifier rules: int2bits-neg-num: i < 0 ⊦ int2bits((* i)) = sgn(bitsinvert(uint2bits(abs(i))) +1);%uint2bits-one: ⊦ uint2bits(1) = false + true;%int2bits-zero: ⊦ int2bits(0) = false ';%n ≠ 0 ⊦ mklist(false, (* n)) = false ' + mklist(false, n -1);% ⊦ j < 0 → (j % 2 ≠ ~1 ↔ j % 2 = 0);% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bitsinvert(false ' + bits) = true + bitsinvert(bits);% ⊦ bitsinvert(true ') = false ';% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (bits + false ')+1 = bits + true;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ sgn(true ' + true ') = true ';% ⊦ 0 < n → fillsgn(n, boolvar ') = mklist(boolvar, n);%n ≠ 0 ⊦ mklist(true, (* n)) = true ' + mklist(true, n -1);% ⊦ mklist(boolvar, 0) = [];% ⊦ bits + [] = bits;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0; Used formulas: j % 2 = ~1