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Proof step 22 from proof uint2int-rest (previous step)

uint2bits(i) = false ' + true ' + bits, 2 ^ (2 + n→i(# bits)) = 1 + bits2uint(bitsinvert(bits)) + 2 ^ (1 + n→i(# bits)) + i, 0 < i ⊦ 2 ^ (1 + n→i(# bits)) = 1 + bits2uint(bitsinvert(bits)) + i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 24:
0 < 2 + n→i(# bits), uint2bits(i) = false ' + true ' + bits, 2 ^ (2 + n→i(# bits))-1 * 2 = 1 + bits2uint(bitsinvert(bits)) + 2 ^ (1 + n→i(# bits)) + i, 0 < i ⊦ 2 ^ (1 + n→i(# bits)) = 1 + bits2uint(bitsinvert(bits)) + i

Rule argument

seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [2 + n→i(# bits), 2] rotate: F spec: int-pot inst: name: Pot-pos

Additional information

Used simplifier rules: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;%i < 0 ⊦ (* i) < n→i(n);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 2 + n→i(# bits), 2