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Proof step 17 from proof int2bytes-rec-pos (previous step)

uint2bits(i) = uint2bits(i / 256) + uint2bits(i % 256).rest, 9 ≤ # uint2bits(i % 256), 255 < i, 0 < i, 0 ≤ i, # uint2bits(i % 256).rest + # uint2bits(i / 256) ≤ 8 ⊦ bits2bytes(uint2bits(i)) = bits2bytes(uint2bits(i / 256)) + bits2bytes(int2bits(i % 256)).last '

User applied rule insert elim lemma

And closed the goal!

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [uint2bits(i % 256), boolvar, bits] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: ⊦ boolvar + bits = boolvar ' + bits;% ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i % j;%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;%n0 < n ⊦ (* n) ≤ m0 + (* n0) ↔ n - n0 ≤ m0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)% ⊦ m + n ≤ m ↔ n = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i / j;%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: uint2bits(i % 256), boolvar, bits