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Proof step 40 from proof lastn-fill-sgn (previous step)

¬(bits0 ≠ [] ∧ (bits0.first ↔ ¬ false)), # bits0 = # fillsgn(# bits0, sgn(false ' + bits0)), # sgn(false ' + bits0) + 1 < # bits1 + # bits0, # sgn(false ' + bits0) < # bits0, # sgn(false ' + bits0) < # bits1 + # bits0 ⊦ bits1 = [], bits1 + bits0 = [], fillsgn(# bits0, sgn(false ' + bits0)) = bits0, bits0 = [], true ∈ bits1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
# bits0 = # fillsgn(# bits0, sgn(false ' + bits0)), # sgn(false ' + bits0) + 1 < # bits1 + # bits0, # sgn(false ' + bits0) < # bits0, # sgn(false ' + bits0) < # bits1 + # bits0 ⊦ bits1 = [], bits1 + bits0 = [], fillsgn(# bits0, sgn(false ' + bits0)) = bits0, bits0 = [], true ∈ bits1, bits0.first

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;