[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 18 from proof bitsand-cast (previous step)

n = # fillsgn(n, mklist(boolvar, n0) + boolvar0 ' + bits1), sgn(mklist(boolvar, n0) + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n0 + 1 + # bits1 < n ⊦ lastn(n, fillsgn(n, bitsand(boolvar ' + boolvar0 ' + bits1, bits0))) = lastn(n, fillsgn(n, bitsand(mklist(boolvar, n0) + boolvar0 ' + bits1, bits0))), bits0 = [], n0 = 0, boolvar ↔ boolvar0, ¬ false ∈ mklist(boolvar, n0) ∧ boolvar0 ∧ ¬ false ∈ bits1, ¬ true ∈ mklist(boolvar, n0) ∧ ¬ boolvar0 ∧ ¬ true ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ n ≠ 0 → mklist(boolvar, n) = mklist(boolvar, n -1) + boolvar '
Proof step 20:
n0 ≠ 0, n = # fillsgn(n, (mklist(boolvar, n0 -1) + boolvar ') + boolvar0 ' + bits1), sgn((mklist(boolvar, n0 -1) + boolvar ') + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n0 + 1 + # bits1 < n ⊦ lastn(n, fillsgn(n, bitsand(boolvar ' + boolvar0 ' + bits1, bits0))) = lastn(n, fillsgn(n, bitsand((mklist(boolvar, n0 -1) + boolvar ') + boolvar0 ' + bits1, bits0))), bits0 = [], n0 = 0, boolvar ↔ boolvar0, ¬ false ∈ mklist(boolvar, n0 -1) + boolvar ' ∧ boolvar0 ∧ ¬ false ∈ bits1, ¬ true ∈ mklist(boolvar, n0 -1) + boolvar ' ∧ ¬ boolvar0 ∧ ¬ true ∈ bits1

Rule argument

seq: ⊦ n ≠ 0 → mklist(boolvar, n) = mklist(boolvar, n -1) + boolvar ' subst: [n, boolvar] → [n0, boolvar] rotate: F spec: list-last inst: bitlista name: mk-last-02

Additional information

Used terms: n0, boolvar