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Proof step 12 from proof ubits2ubits-def (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
bits2uint(bits0) = 0, ∀ bits1. # bits1 < #(bits0 + false ') → true → uint2bits(bits2uint(bits1)) = sgn(false ' + bits1) ⊦ false ' = sgn(false ' + bits0 + false ')

Rule argument

Additional information

Used simplifier rules: bits2uint-not-neg: ⊦ bits2uint(bits) ≤ 0 ↔ bits2uint(bits) = 0;%uint2bits-zero: ⊦ uint2bits(0) = false ';% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0);