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Proof step 2 from proof int2unit-inv-rest (previous step)

0 < i ⊦ 2 ^ (n→i(# uint2bits(i)) - 1) = bits2uint(bitsinvert(int2bits(i).rest)) + i + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ bits ≠ [] ∧ bits.first → bits2uint(bitsinvert(bits)) = ~ bits2int(bits) - 1
Proof step 4:
¬(int2bits(i).rest ≠ [] ∧ int2bits(i).rest.first), 0 < i ⊦ 2 ^ (n→i(# uint2bits(i)) - 1) = bits2uint(bitsinvert(int2bits(i).rest)) + i + 1
Proof step 12:
int2bits(i).rest ≠ [] ∧ int2bits(i).rest.first, 0 < i ⊦ 2 ^ (n→i(# uint2bits(i)) - 1) = (~ bits2int(int2bits(i).rest) - 1) + i + 1

Rule argument

name: bits2uint-inv-pos rotate: F subst: [bits] → [int2bits(i).rest]

Additional information

Used terms: int2bits(i).rest