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Proof step 7 from proof bits2uint-split (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ boolvar → bits2uint(bits + boolvar ') = bits2uint(bits) * 2 + 1
Proof step 9:
¬ boolvar, ∀ bits2, bits. # bits2 < #(bits1 + boolvar ') → true → bits2uint(bits + bits2) = bits2uint(bits) * 2 ^ n→i(# bits2) + bits2uint(bits2) ∨ bits2 = [] ⊦ bits2uint(bits + bits1 + boolvar ') = bits2uint(bits1 + boolvar ') + 2 ^ (n→i(# bits1) + 1) * bits2uint(bits)
Proof step 16:
boolvar, ∀ bits2, bits. # bits2 < #(bits1 + boolvar ') → true → bits2uint(bits + bits2) = bits2uint(bits) * 2 ^ n→i(# bits2) + bits2uint(bits2) ∨ bits2 = [] ⊦ bits2uint(bits + bits1 + boolvar ') = (bits2uint(bits1) * 2 + 1) + 2 ^ (n→i(# bits1) + 1) * bits2uint(bits)

Rule argument

name: bits2uint-rec-02 rotate: F subst: [boolvar, bits] → [boolvar, bits1]

Additional information

Used terms: boolvar, bits1