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Proof step 3 from proof ubits2ubits-def (previous step)

∀ bits0. # bits0 < # bits → true → uint2bits(bits2uint(bits0)) = sgn(false ' + bits0) ⊦ uint2bits(bits2uint(bits)) = sgn(false ' + bits)

User applied rule cut formula

And obtained the following new goals

Proof step 4:
∀ bits0. # bits0 < # bits → true → uint2bits(bits2uint(bits0)) = sgn(false ' + bits0) ⊦ bits = [], uint2bits(bits2uint(bits)) = sgn(false ' + bits)

Rule argument

fma: bits = []

Additional information

Used simplifier rules: bits2uint-base: ⊦ bits2uint([]) = 0;%uint2bits-zero: ⊦ uint2bits(0) = false ';% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ sgn(boolvar ') = boolvar ';% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0; Used formulas: bits = []