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Proof step 43 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), (bitsinvert(bits1) + true ').first ⊦ bits1 = [], true ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first)
Proof step 45:
bitsinvert(bits1) ≠ [], uint2bits(~ i) = false ' + bits1 + true ', bitsinvert(uint2bits(~ i)) +1 = true ' + bitsinvert(bits1) + true ', i < 0, i < ~1, false ∈ uint2bits(~ i), bitsinvert(bits1).first ⊦ bits1 = [], true ∈ bits1

Rule argument

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

Additional information

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