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Proof step 29 from proof uint2bits-add-high-02 (previous step)

j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 ≤ j0 + 2 ^ i, 1 < j, 0 < j ⊦ uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0).rest) = sgn(uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0).rest))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ 0 < j → sgn(uint2bits(j) + bits) = uint2bits(j) + bits

Rule argument

name: uint2bits-sgn-02 rotate: F subst: [bits, j] → [fillsgn(i→n(i), int2bits(j0).rest), j - 1]

Additional information

Used simplifier rules: uint2bits-zero: ⊦ uint2bits(0) = false ';% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < i → (i ≤ 1 ↔ i = 1);% ⊦ i = j → i - j = 0; Used terms: fillsgn(i→n(i), int2bits(j0).rest), j - 1