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Proof step 6 from proof uint2bits-sgn-2pot (previous step)

uint2bits(j) = false ' + true ' + bits, false ∈ false ' + true ' + bits, 0 < j, ∀ i. ¬ i < 0 → j ≠ 2 ^ i ⊦ sgn(bitsinvert(false ' + true ' + bits) +1) = bitsinvert(false ' + true ' + bits) +1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ true ∈ bits → sgn(bitsinvert(false ' + true ' + bits) +1) = true ' + false ' + bitsinvert(bits) +1
Proof step 8:
¬ true ∈ bits, uint2bits(j) = false ' + true ' + bits, false ∈ false ' + true ' + bits, 0 < j, ∀ i. ¬ i < 0 → j ≠ 2 ^ i ⊦ sgn(bitsinvert(false ' + true ' + bits) +1) = bitsinvert(false ' + true ' + bits) +1

Rule argument

seq: ⊦ true ∈ bits → sgn(bitsinvert(false ' + true ' + bits) +1) = true ' + false ' + bitsinvert(bits) +1 subst: [bits] → [bits] rotate: F spec: bitopsaux inst: name: sgn-negint

Additional information

Used simplifier rules: ⊦ bitsinvert(false ' + bits) = true + bitsinvert(bits);% ⊦ bitsinvert(true ' + bits) = false + bitsinvert(bits);% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (bits + false ' + bits0)+1 = bits + (false ' + bits0)+1;%⊦ true ∈ bits0 → (bits + bitsinvert(bits0))+1 = bits + bitsinvert(bits0) +1;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1; Used terms: bits