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Proof step 21 from proof band-max (previous step)

1 < bits2int(bitsand(false ' + true ', int2bits(j))), 0 < bits2int(bitsand(false ' + true ', int2bits(j))), ∀ i0, j. i→n(i0) < i→n(1) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ j = ~1, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)
Proof step 23:
¬(1 < #(false ' + true ') ∧ 1 < # int2bits(j)), 1 < bits2int(bitsand(false ' + true ', int2bits(j))), 0 < bits2int(bitsand(false ' + true ', int2bits(j))), ∀ i0, j. i→n(i0) < i→n(1) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ j = ~1, j = 0
Proof step 25:
1 < #(false ' + true ') ∧ 1 < # int2bits(j), 1 < bits2int(bitsand((false ' + true ').butlast, int2bits(j).butlast) + ((false ' + true ').last ∧ int2bits(j).last)), 0 < bits2int(bitsand((false ' + true ').butlast, int2bits(j).butlast) + ((false ' + true ').last ∧ int2bits(j).last)), ∀ i0, j. i→n(i0) < i→n(1) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ j = ~1, j = 0

Rule argument

name: and-rec rotate: F subst: [bits0, bits] → [int2bits(j), false ' + true ']

Additional information

Used terms: int2bits(j), false ' + true '