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Proof step 3 from proof uint2bits-2pot-03 (previous step)

bits2uint(uint2bits(i)) = bits2uint(false ' + true ' + bits), uint2bits(i) = false ' + true ' + bits, false ∈ uint2bits(i), 0 ≤ i ⊦ i = 2 ^ n→i(# bits), true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ¬ true ∈ bits → bits2uint(false ' + true ' + bits) = 2 ^ n→i(# bits)
Proof step 5:
¬ true ∈ bits, bits2uint(uint2bits(i)) = 2 ^ n→i(# bits), uint2bits(i) = false ' + true ' + bits, false ∈ uint2bits(i), 0 ≤ i ⊦ i = 2 ^ n→i(# bits), true ∈ bits

Rule argument

name: bits2uint-2pot-01 rotate: F subst: [bits] → [bits]

Additional information

Used terms: bits