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Proof step 3 from proof uint2bits-pred (previous step)

0 < j, ∀ j0. i→n(j0) < i→n(j) → 0 < j0 → uint2bits(j0 - 1) = sgn(bitsinvert(bitsinvert(uint2bits(j0)) +1)) ⊦ uint2bits(j - 1) = sgn(bitsinvert(bitsinvert(uint2bits(j)) +1))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: uint2bits-rec-01 rotate: F subst: [i] → [j - 1]

Additional information

Used simplifier rules: uint2bits-zero: ⊦ uint2bits(0) = false ';%uint2bits-one: ⊦ uint2bits(1) = false + true;%uint2bits-pos-num: 1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < i → (i ≤ 1 ↔ i = 1);% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ 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 ';% ⊦ bitsinvert(true ' + bits) = false + bitsinvert(bits);% ⊦ sgn(false ' + false ') = false ';% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ bitsinvert(false ') = true ';% ⊦ (bits + true ')+1 = bits +1 + false;% ⊦ sgn(boolvar ' + boolvar ' + bits) = sgn(boolvar ' + bits);% ⊦ sgn(false ' + true ') = false ' + true ';% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1; Used terms: j - 1