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Proof step 15 from proof uint2bits-falsein (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
bits = boolvar + bits0, uint2bits(i) = false ' + bitsinvert(bits0) + true ', 0 ≤ i, 0 < i, 1 < i, boolvar, false ∈ uint2bits(i) ⊦ bits = [], false ∈ bits

Rule argument

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

Additional information

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