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Proof step 35 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ bits0 ≠ [] ∧ (¬ bits0.first) ∈ bits → sgn(bits + bits0) = sgn(bits) + bits0
Proof step 37:
¬(true ' + bits0 ≠ [] ∧ (¬ (true ' + bits0).first) ∈ 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(bitsinvert(bits1) + true ' + bits0).rest
Proof step 50:
true ' + bits0 ≠ [] ∧ (¬ (true ' + bits0).first) ∈ 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(bitsinvert(bits1)) + true ' + bits0).rest

Rule argument

seq: ⊦ bits0 ≠ [] ∧ (¬ bits0.first) ∈ bits → sgn(bits + bits0) = sgn(bits) + bits0 subst: [bits0, bits] → [true ' + bits0, bitsinvert(bits1)] rotate: F spec: bitopsaux inst: name: sgn-append-06

Additional information

Used terms: true ' + bits0, bitsinvert(bits1)