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Proof step 17 from proof bits2uint-split (previous step)

∀ bits2, bits. # bits2 < #(bits1 + true ') → true → bits2uint(bits + bits2) = bits2uint(bits) * 2 ^ n→i(# bits2) + bits2uint(bits2) ∨ bits2 = [] ⊦ bits2uint(bits + bits1) * 2 = bits2uint(bits1) * 2 + 2 ^ (n→i(# bits1) + 1) * bits2uint(bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j
Proof step 19:
0 ≤ n→i(# bits1), ∀ bits2, bits. # bits2 < #(bits1 + true ') → true → bits2uint(bits + bits2) = bits2uint(bits) * 2 ^ n→i(# bits2) + bits2uint(bits2) ∨ bits2 = [] ⊦ bits2uint(bits + bits1) * 2 = bits2uint(bits1) * 2 + (2 ^ n→i(# bits1) * 2) * bits2uint(bits)

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [n→i(# bits1), 2] rotate: F spec: int-pot inst: name: succ

Additional information

Used simplifier rules: ⊦ 0 ≤ n→i(n); Used terms: n→i(# bits1), 2