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Proof step 13 from proof uint2bits-sgn-2pot (previous step)

uint2bits(bits2uint(false ' + true ' + bits)) = false ' + true ' + bits, 0 ≤ bits2uint(false ' + true ' + bits), 0 < bits2uint(false ' + true ' + bits), ∀ i. ¬ i < 0 → bits2uint(false ' + true ' + bits) ≠ 2 ^ i ⊦ sgn(true ' + bits) = true ' + true ' + bits, true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ ¬ true ∈ bits → bits2uint(false ' + true ' + bits) = 2 ^ n→i(# bits)
Proof step 15:
¬ true ∈ bits, uint2bits(2 ^ n→i(# bits)) = false ' + true ' + bits, 0 ≤ 2 ^ n→i(# bits), 0 < 2 ^ n→i(# bits), ∀ i. ¬ i < 0 → 2 ^ n→i(# bits) ≠ 2 ^ i ⊦ sgn(true ' + bits) = true ' + true ' + bits, true ∈ bits

Rule argument

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

Additional information

Used terms: bits