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Proof step 17 from proof uint2bits-falsein (previous step)

uint2bits(i) = false ' + bitsinvert(bits0) + true ', 0 ≤ i, 0 < i, 1 < i, false ∈ uint2bits(i) ⊦ false ∈ bits0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ bits ≠ [] → bitsinvert(bits) = (¬ bits.first)' + bitsinvert(bits.rest)
Proof step 19:
¬ bits0 ≠ [], uint2bits(i) = false ' + bitsinvert(bits0) + true ', 0 ≤ i, 0 < i, 1 < i, false ∈ uint2bits(i) ⊦ false ∈ bits0
Proof step 22:
bits0 ≠ [], uint2bits(i) = false ' + ((¬ bits0.first)' + bitsinvert(bits0.rest)) + true ', 0 ≤ i, 0 < i, 1 < i, false ∈ uint2bits(i) ⊦ false ∈ bits0

Rule argument

seq: ⊦ bits ≠ [] → bitsinvert(bits) = (¬ bits.first)' + bitsinvert(bits.rest) subst: [bits] → [bits0] rotate: F spec: bitopsaux inst: name: inv-rec-01

Additional information

Used terms: bits0