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Proof step 4 from proof and-011x-neg (previous step)

bitsand(false ' + bits0, true ' + bits2) = false ' + bits1 ⊦ 2 ^ n→i(# bits0) = 1 + bits2uint(bitsinvert(bits2)) % 2 ^ n→i(# bits0) + bits2uint(bits1), false ∈ bits0

User applied rule induction

And obtained the following new goals

Proof step 5:
bitsand(false ' + bits0, true ' + bits2) = false ' + bits1, ∀ bits, bits2, bits1. # bits < # bits0 → bitsand(false ' + bits, true ' + bits2) = false ' + bits1 → 2 ^ n→i(# bits) = 1 + bits2uint(bitsinvert(bits2)) % 2 ^ n→i(# bits) + bits2uint(bits1) ∨ false ∈ bits ⊦ 2 ^ n→i(# bits0) = 1 + bits2uint(bitsinvert(bits2)) % 2 ^ n→i(# bits0) + bits2uint(bits1) ∨ false ∈ bits0

Rule argument

indvar: # bits0 wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # bits0