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Proof step 46 from proof int2bits-falsein-01 (previous step)

uint2bits(~ i) = false ' + bits1 + true ', bitsinvert(uint2bits(~ i)) +1 = true ' + bitsinvert(bits1) + true ', i < 0, i < ~1, false ∈ uint2bits(~ i), bitsinvert(bits1).first ⊦ bits1 = [], true ∈ bits1

User applied rule insert elim lemma

And obtained the following new goals

Proof step 47:
bitsinvert(bits1) = boolvar + bits ∧ bitsinvert(bits1) ≠ [], uint2bits(~ i) = false ' + bits1 + true ', bitsinvert(uint2bits(~ i)) +1 = true ' + bitsinvert(bits1) + true ', i < 0, i < ~1, false ∈ uint2bits(~ i), boolvar ⊦ bits1 = [], true ∈ bits1

Rule argument

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

Additional information

Used simplifier rules: ⊦ bitsinvert(bits) = [] ↔ bits = [];%⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0); (elim) Used terms: bitsinvert(bits1), boolvar, bits