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Proof step 33 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) ⊦ bits1 = [], bitsinvert(bits1).first, (bitsinvert(bits1) + true ').first, true ∈ bits1

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] → [bitsinvert(bits1), boolvar, bits] rotate: T spec: list-data inst: bitlista name: elim-1

Additional information

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