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Proof step 31 from proof prefix-at (previous step)

# x = # lax2 + # lax1 + 1, # x + # z = # lax2 + (# lax1 + # lax) + 1, st1[m] = mkblock(x + z, (lax2 + @(m0, m1) ' + lax1) + lax, m3), st0[m] = mkblock(x, lax2 + @(m0, m1) ' + lax1, m2), m ∈ st1, m ∈ st0, ∀ n. n ∈ st0 → n ∈ st1 ⊦ x[# lax2] = (x + z)[# lax2], @(m0, m1) ∈ lax2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ n < # x → (x + y)[n] = x[n]
Proof step 33:
# x = # lax2 + # lax1 + 1, # x + # z = # lax2 + (# lax1 + # lax) + 1, st0[m] = mkblock(x, lax2 + @(m0, m1) ' + lax1, m2), st1[m] = mkblock(x + z, (lax2 + @(m0, m1) ' + lax1) + lax, m3), m ∈ st0, m ∈ st1, ∀ n. n ∈ st0 → n ∈ st1 ⊦ x[# lax2] = (x + z)[# lax2], # lax2 < # x, @(m0, m1) ∈ lax2

Rule argument

spec: list-del name: get-append-less seq: ⊦ n < # x → (x + y)[n] = x[n] subst: [n, y, x] → [# lax2, z, x] flags: <all paths>

Additional information

Used terms: # lax2, z, x