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Proof step 35 from proof ubits2ubits-def (previous step)

0 < bits2uint(bits0), ∀ 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 ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ 0 ≤ i → (2 * i + 1) / 2 = i
Proof step 37:
0 ≤ bits2uint(bits0), 0 < bits2uint(bits0), ∀ bits1. # bits1 < #(bits0 + true ') → true → uint2bits(bits2uint(bits1)) = sgn(false ' + bits1) ⊦ uint2bits(bits2uint(bits0)) + ((bits2uint(bits0) * 2 + 1) % 2 = 1)' = sgn(false ' + bits0 + true ')

Rule argument

seq: ⊦ 0 ≤ i → (2 * i + 1) / 2 = i subst: [i] → [bits2uint(bits0)] rotate: F spec: int-div inst: name: div-two

Additional information

Used simplifier rules: bits2uint-not-neg-01: ⊦ ¬ bits2uint(bits) < 0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i * j = j * i;% ⊦ i + j = j + i; Used terms: bits2uint(bits0)