[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 7 from proof bits2int-lasteq (previous step)

⊦ bits0 = [], bits2int((boolvar0 ' + bits1) + boolvar ') = bits2int(bits0 + boolvar ') ↔ bits2int(boolvar0 ' + bits1) = bits2int(bits0), boolvar ∧ ¬ boolvar0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ boolvar ∧ bits.first ∧ bits ≠ [] → bits2int(bits + boolvar ') = ~(bits2uint(bitsinvert(bits.rest)) * 2 + 1)
Proof step 9:
¬(boolvar ∧ (boolvar0 ' + bits1).first ∧ boolvar0 ' + bits1 ≠ []) ⊦ bits0 = [], bits2int((boolvar0 ' + bits1) + boolvar ') = bits2int(bits0 + boolvar ') ↔ bits2int(boolvar0 ' + bits1) = bits2int(bits0), boolvar ∧ ¬ boolvar0
Proof step 26:
boolvar ∧ (boolvar0 ' + bits1).first ∧ boolvar0 ' + bits1 ≠ [] ⊦ bits0 = [], ~(bits2uint(bitsinvert((boolvar0 ' + bits1).rest)) * 2 + 1) = bits2int(bits0 + boolvar ') ↔ bits2int(boolvar0 ' + bits1) = bits2int(bits0), boolvar ∧ ¬ boolvar0

Rule argument

name: bits2int-rec-01 rotate: F subst: [boolvar, bits] → [boolvar, boolvar0 ' + bits1]

Additional information

Used terms: boolvar, boolvar0 ' + bits1