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Proof step 7 from proof uint2bits-2pot-05 (previous step)

uint2bits(i) = false ' + bits, 0 ≤ i, false ∈ uint2bits(i) ⊦ bits = [], 2 ^ n→i(# bits) = i + 1, false ∈ bits

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
⊦ ¬ false ∈ bits ∧ 0 ≤ i → (uint2bits(i) = false ' + true ' + bits ↔ i = 2 ^ (n→i(# bits) + 1) - 1)
Proof step 9:
¬ false ∈ bits.rest ∧ 0 ≤ i → (uint2bits(i) = false ' + true ' + bits.rest ↔ i = 2 ^ (n→i(# bits.rest) + 1) - 1), uint2bits(i) = false ' + bits, 0 ≤ i, false ∈ uint2bits(i) ⊦ bits = [], 2 ^ n→i(# bits) = i + 1, false ∈ bits

Rule argument

name: uint2bits-2pot-04 subst: [bits, i] → [bits.rest, i]

Additional information

Used terms: bits.rest, i