[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 21 from proof fill-sgn-01 (previous step)

# bits + n1 = 1 + n, ∀ n0. ¬ n0 ≤ # bits + # bits1 → fillsgn(n0, sgn(bits + (¬ boolvar)' + bits1)) = fillsgn(n0, bits + (¬ boolvar)' + bits1) ⊦ boolvar ' + mklist(boolvar, n) = mklist(boolvar, n1) + bits, n1 = 0, (¬ boolvar) ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ ¬ boolvar ∈ bits ↔ mklist(¬ boolvar, # bits) = bits
Proof step 23:
# bits + n1 = 1 + n, ∀ n0. ¬ n0 ≤ # bits + # bits1 → fillsgn(n0, sgn(bits + (¬ boolvar)' + bits1)) = fillsgn(n0, bits + (¬ boolvar)' + bits1) ⊦ boolvar ' + mklist(boolvar, n) = mklist(boolvar, n1) + bits, n1 = 0, mklist(¬ ¬ boolvar, # bits) ≠ bits

Rule argument

seq: ⊦ ¬ boolvar ∈ bits ↔ mklist(¬ boolvar, # bits) = bits subst: [bits, boolvar] → [bits, ¬ boolvar] rotate: F spec: bitlista inst: name: mklist-intro

Additional information

Used terms: bits, ¬ boolvar