[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 997 from proof bitsand-cast (previous step)

mklist(false, # bits1) = bits1, # bits0 ≤ # bits1, bits0.first ⊦ bits1 = [], bits2 + bits1 = [], bits1 = lastn(# bits1, fillsgn(# bits1, bits2 + bitsand(bits1, bits0))), bits0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 998:
⊦ ¬ true ∈ bits ∧ (# bits ≤ # bits0 ∨ bits0.first) ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bits
Proof step 999:
¬(¬ true ∈ bits1 ∧ (# bits1 ≤ # bits0 ∨ bits0.first) ∧ bits1 ≠ [] ∧ bits0 ≠ []), mklist(false, # bits1) = bits1, # bits0 ≤ # bits1, bits0.first ⊦ bits1 = [], bits2 + bits1 = [], bits1 = lastn(# bits1, fillsgn(# bits1, bits2 + bitsand(bits1, bits0))), bits0 = []
Proof step 1002:
¬ true ∈ bits1 ∧ (# bits1 ≤ # bits0 ∨ bits0.first) ∧ bits1 ≠ [] ∧ bits0 ≠ [], mklist(false, # bits1) = bits1, # bits0 ≤ # bits1, bits0.first ⊦ bits1 = [], bits2 + bits1 = [], bits1 = lastn(# bits1, fillsgn(# bits1, bits2 + bits1)), bits0 = []

Rule argument

name: bitsand-zeros rotate: F subst: [bits0, bits] → [bits0, bits1]

Additional information

Used terms: bits0, bits1