[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 54 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)).rest, false ∈ bits0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 55:
⊦ ¬ false ∈ bits ∧ bits ≠ [] → sgn(bits) = true '
Proof step 56:
¬(¬ 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, true ∈ bits1 ⊦ bits1 = [], true ∈ bits0, false ∈ sgn(bitsinvert(bits1)).rest, false ∈ bits0

Rule argument

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

Additional information

Used simplifier rules: ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ boolvar '.rest = [];% ⊦ ¬ boolvar ∈ [];% ⊦ false ∈ bitsinvert(bits) ↔ true ∈ bits; Used terms: bitsinvert(bits1)