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Proof step 23 from proof ubits2ubits-def (previous step)

∀ bits1. # bits1 < #(bits0 + true ') → true → uint2bits(bits2uint(bits1)) = sgn(false ' + bits1) ⊦ uint2bits(bits2uint(bits0) * 2 + 1) = sgn(false ' + bits0 + true ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ 1 < i → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1)
Proof step 25:
¬ 1 < bits2uint(bits0) * 2 + 1, ∀ bits1. # bits1 < #(bits0 + true ') → true → uint2bits(bits2uint(bits1)) = sgn(false ' + bits1) ⊦ uint2bits(bits2uint(bits0) * 2 + 1) = sgn(false ' + bits0 + true ')
Proof step 34:
1 < bits2uint(bits0) * 2 + 1, ∀ bits1. # bits1 < #(bits0 + true ') → true → uint2bits(bits2uint(bits1)) = sgn(false ' + bits1) ⊦ uint2bits((bits2uint(bits0) * 2 + 1) / 2) + ((bits2uint(bits0) * 2 + 1) % 2 = 1) = sgn(false ' + bits0 + true ')

Rule argument

name: uint2bits-rec rotate: F subst: [i] → [bits2uint(bits0) * 2 + 1]

Additional information

Used terms: bits2uint(bits0) * 2 + 1