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Proof step 12 from proof uint2bits-falsein (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ bits ≠ [] → bitsinvert(bits) = (¬ bits.first)' + bitsinvert(bits.rest)
Proof step 14:
bits ≠ [], uint2bits(i) = ((¬ bits.first)' + bitsinvert(bits.rest)) + true ', 1 < i, 0 < i, 0 ≤ i ⊦ false ∈ bits

Rule argument

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

Additional information

Used simplifier rules: uint2bits-not-one: 0 ≤ i ⊦ uint2bits(i) ≠ true ';% ⊦ bitsinvert([]) = [];% ⊦ [] + bits = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ boolvar ∈ []; Used terms: bits