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Proof step 50 from proof int2bytes-rec-pos (previous step)

# uint2bits(i % 256) = 9, uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, i % 256 ≤ 127, 0 ≤ i, 0 < i, 255 < i ⊦ bits2int(fillsgn(9, uint2bits(i % 256)).rest) = i % 256, i2b(bits2int(fillsgn(9, uint2bits(i % 256)).rest)) = i2b(i % 256), fillsgn(9, uint2bits(i % 256)) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 52:
9 ≤ # uint2bits(i % 256), # uint2bits(i % 256) = 9, uint2bits(i) = uint2bits(i / 256) + uint2bits(i % 256).rest, i % 256 ≤ 127, 0 ≤ i, 0 < i, 255 < i ⊦ bits2int(uint2bits(i % 256).rest) = i % 256, i2b(bits2int(uint2bits(i % 256).rest)) = i2b(i % 256), uint2bits(i % 256) = []

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [uint2bits(i % 256), 9] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n → ¬ n < m; Used terms: uint2bits(i % 256), 9