[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 41 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8 + 1) = # int2bits(j % 2 ^ (i * 8)), j % 2 ^ (i * 8) = 0 ∨ j % 2 ^ (i * 8) = ~1, 0 < j, 2 ^ (i * 8) ≤ j, 0 < i, 0 ≤ i, 0 ≤ j, i→n(i * 8 + 1) ≤ 1 + 8 * i→n(i) ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + (mklist(¬ 0 ≤ j % 2 ^ (i * 8), 1 + 8 * i→n(i) - i→n(i * 8 + 1)) + int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest

User applied rule case distinction

And closed the goal!

Rule argument

pos: left 2

Additional information

Used simplifier rules: ⊦ int2bits(0) = false ';%i < 0 ⊦ int2bits((* i)) = sgn(bitsinvert(uint2bits(abs(i))) +1);% ⊦ uint2bits(1) = false + true;% ⊦ 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 ';% ⊦ # boolvar ' = 0 +1;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);%0 ≤ i ⊦ i→n(i) = (* m) ↔ i = n→i(m);% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ 0 < i → (i * j = 0 ↔ j = 0);