[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 17 from proof intshiftrzero-prop-01 (previous step)

~2147483648 ≤ i, i < 0 ⊦ band(j, 31) = 0, bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) = (i i>> j) + bits2int(int2bits(2) + mklist(false, i→n(band(31, 31 - j)))), false ∈ int2bits(31).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(i - j, i) = i - band(j, i)
Proof step 19:
¬ false ∈ int2bits(31).rest ∧ 0 ≤ 31, ~2147483648 ≤ i, i < 0 ⊦ band(j, 31) = 0, bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) = (i i>> j) + bits2int(int2bits(2) + mklist(false, i→n(31 - band(j, 31)))), false ∈ int2bits(31).rest

Rule argument

name: band-011x-eq-01 rotate: F subst: [j, i] → [j, 31]

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i); Used terms: j, 31