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Proof step 6 from proof cast-law-shift-snd-zr (previous step)

¬(n→i((# int2bits(31))-1) ≤ i ∧ 0 ≤ 31), 5 ≤ i, 0 < i, 0 ≤ i ⊦ j0 i>>> j = bits2int(sublist(0, # fillsgn(32, int2bits(j0)), mklist(false, i→n(band(cast(i, j), 31))) + fillsgn(32, int2bits(j0))))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → int2bits(i) = uint2bits(i) subst: [i] → [31] rotate: F spec: int2bits inst: name: int2bits-pos

Additional information

Used simplifier rules: 1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);% ⊦ uint2bits(1) = false + true;% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bits + boolvar = bits + boolvar ';% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 31