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Proof step 38 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 ⊦ bits1 = [], true ∈ bits0, false ∈ sgn(bitsinvert(bits1) + true ' + bits0).rest, true ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ ¬ false ∈ bits ∧ bits ≠ [] → sgn(bits + bits0) = sgn(true ' + bits0)
Proof step 40:
¬ false ∈ bitsinvert(bits1) ∧ 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 ⊦ bits1 = [], true ∈ bits0, false ∈ sgn(true ' + true ' + bits0).rest, true ∈ bits1

Rule argument

seq: ⊦ ¬ false ∈ bits ∧ bits ≠ [] → sgn(bits + bits0) = sgn(true ' + bits0) subst: [bits0, bits] → [true ' + bits0, bitsinvert(bits1)] rotate: F spec: bitopsaux inst: name: sgn-append-05

Additional information

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