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Proof step 90 from proof byte-law-righthift-not (previous step)

31 = # int2bits(~128) + n, i2b(bits2uint(mklist(false, n) + firstn(# int2bits(~128), int2bits(128)))) = i2b(bits2uint(firstn(31, (mklist(true, n) + true ') + int2bits(~128)))), 32 = n + # int2bits(128), n ≤ 32, n ≤ 31, # int2bits(~128) ≤ 32, # int2bits(128) ≤ 32 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 91:
⊦ m ≤ # bits + # bits0 ∧ # bits ≤ m → firstn(m, bits + bits0) = bits + firstn(m - # bits, bits0)
Proof step 92:
¬(31 ≤ #(mklist(true, n) + true ') + # int2bits(~128) ∧ #(mklist(true, n) + true ') ≤ 31), 31 = # int2bits(~128) + n, i2b(bits2uint(mklist(false, n) + firstn(# int2bits(~128), int2bits(128)))) = i2b(bits2uint(firstn(31, (mklist(true, n) + true ') + int2bits(~128)))), 32 = n + # int2bits(128), n ≤ 32, n ≤ 31, # int2bits(~128) ≤ 32, # int2bits(128) ≤ 32 ⊦
Proof step 95:
31 ≤ #(mklist(true, n) + true ') + # int2bits(~128) ∧ #(mklist(true, n) + true ') ≤ 31, 31 = # int2bits(~128) + n, i2b(bits2uint(mklist(false, n) + firstn(# int2bits(~128), int2bits(128)))) = i2b(bits2uint((mklist(true, n) + true ') + firstn(31 - #(mklist(true, n) + true '), int2bits(~128)))), 32 = n + # int2bits(128), n ≤ 32, n ≤ 31, # int2bits(~128) ≤ 32, # int2bits(128) ≤ 32 ⊦

Rule argument

seq: ⊦ m ≤ # bits + # bits0 ∧ # bits ≤ m → firstn(m, bits + bits0) = bits + firstn(m - # bits, bits0) subst: [bits0, bits, m] → [int2bits(~128), mklist(true, n) + true ', 31] rotate: F spec: list-del inst: bitlista name: firstn-app-02

Additional information

Used terms: int2bits(~128), mklist(true, n) + true ', 31