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Proof step 51 from proof int2bits-falsein-01 (previous step)

uint2bits(~ i) = (false ' + bits1) + true ' + bits0, bitsinvert(uint2bits(~ i)) +1 = (true ' + bitsinvert(bits1)) + true ' + bits0, i < 0, i < ~1, false ∈ uint2bits(~ i), (bitsinvert(bits1) + true ').first, true ∈ bits1 ⊦ bits1 = [], true ∈ bits0, false ∈ (sgn(bitsinvert(bits1)) + true ' + bits0).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ bits ≠ [] → (bits + bits0).rest = bits.rest + bits0
Proof step 53:
sgn(bitsinvert(bits1)) ≠ [], uint2bits(~ i) = (false ' + bits1) + true ' + bits0, bitsinvert(uint2bits(~ i)) +1 = (true ' + bitsinvert(bits1)) + true ' + bits0, i < 0, i < ~1, false ∈ uint2bits(~ i), (bitsinvert(bits1) + true ').first, true ∈ bits1 ⊦ bits1 = [], true ∈ bits0, false ∈ sgn(bitsinvert(bits1)).rest + true ' + bits0

Rule argument

seq: ⊦ bits ≠ [] → (bits + bits0).rest = bits.rest + bits0 subst: [bits0, bits] → [true ' + bits0, sgn(bitsinvert(bits1))] rotate: F spec: list inst: bitlista name: rest-01

Additional information

Used simplifier rules: ⊦ sgn(bits) = [] ↔ bits = [];% ⊦ bitsinvert(bits) = [] ↔ bits = []; Used terms: true ' + bits0, sgn(bitsinvert(bits1))