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Proof step 287 from proof bitsand-cast (previous step)

n = # fillsgn(n, bits), # bits0 ≤ # bits, bits0.first, true ∈ bits, # bits < n, # bits0 < n ⊦ bits0 = [], bits = [], lastn(n, fillsgn(n, bits0)) = lastn(n, fillsgn(n, mklist(true, # bits - # bits0) + bits0)), false ∈ bits

User applied rule insert elim lemma

And obtained the following new goals

Proof step 288:
# bits = n0 + # bits0, n = # fillsgn(n, bits), # bits0 ≤ # bits, bits0.first, true ∈ bits, # bits < n, # bits0 < n ⊦ bits0 = [], bits = [], lastn(n, fillsgn(n, bits0)) = lastn(n, fillsgn(n, mklist(true, n0) + bits0)), false ∈ bits

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# bits, # bits0, n0] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # bits, # bits0, n0