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Proof step 2 from proof uint2int-rest (previous step)

0 < i ⊦ i = bits2int(uint2bits(i).rest) + 2 ^ (n→i(# uint2bits(i)) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ bits.first ∧ bits ≠ [] → bits2int(bits) = ~ bits2uint(bitsinvert(true + bits.rest) +1)
Proof step 4:
¬(uint2bits(i).rest.first ∧ uint2bits(i).rest ≠ []), 0 < i ⊦ i = bits2int(uint2bits(i).rest) + 2 ^ (n→i(# uint2bits(i)) - 1)
Proof step 5:
uint2bits(i).rest.first ∧ uint2bits(i).rest ≠ [], 0 < i ⊦ i = ~ bits2uint(bitsinvert(true + uint2bits(i).rest.rest) +1) + 2 ^ (n→i(# uint2bits(i)) - 1)

Rule argument

name: bits2int-neg-01 rotate: F subst: [bits] → [uint2bits(i).rest]

Additional information

Used terms: uint2bits(i).rest