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Proof step 895 from proof bitsand-cast (previous step)

# bits1 = n + # bits0, bits0.first, # bits0 < # bits1, # bits0 < # bits2 + # bits1 ⊦ mklist(true, n) + bits0 = lastn(# bits1, bits2 + mklist(true, n) + bits0), bits1 = [], bits2 + bits1 = [], bits0 = [], n = 0, false ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 896:
⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits)
Proof step 897:
# bits1 ≤ #(mklist(true, n) + bits0), # bits1 = n + # bits0, bits0.first, # bits0 < # bits1, # bits0 < # bits2 + # bits1 ⊦ mklist(true, n) + bits0 = lastn(# bits1, mklist(true, n) + bits0), bits1 = [], bits2 + bits1 = [], bits0 = [], n = 0, false ∈ bits1

Rule argument

seq: ⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits) subst: [bits, bits0, n] → [mklist(true, n) + bits0, bits2, # bits1] rotate: F spec: list-del inst: bitlista name: lastN-append-01

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ m < n → ¬ n < m; Used terms: mklist(true, n) + bits0, bits2, # bits1