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Proof step 10 from proof int2bits-falsein-01 (previous step)

bits.first, uint2bits(~ i) = bits + true ' + bits0, bitsinvert(uint2bits(~ i)) +1 = bitsinvert(bits) + true ' + bits0, i < 0, i < ~1 ⊦ bits = [], true ∈ bits0, false ∈ sgn(bitsinvert(bits) + true ' + bits0).rest

User applied rule insert elim lemma

And closed the goal!

Rule argument

seq: ⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0) subst: [bits, boolvar, bits0] → [bits, boolvar, bits1] rotate: T spec: list-data inst: bitlista name: elim-1

Additional information

Used simplifier rules: uint2bits-first-05: ⊦ j < 0 → uint2bits(~ j) ≠ true ' + bits;% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0); (elim) Used terms: bits, boolvar, bits1