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Proof step 3 from proof lebs-idexpt-below (previous step)

# avol1 = # avol0, n < m0, id○(avol1, avol0, n), m0 + m1 ≤ # avol0 ⊦ lebs(avol1, m0, m1) = lebs(avol0, m0, m1)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
# avol1 = # avol0, n < m0, id○(avol1, avol0, n), m0 + m +1 ≤ # avol0, ∀ avol1, avol0, n, m0. # avol1 = # avol0 ∧ n < m0 ∧ id○(avol1, avol0, n) ∧ m0 + m ≤ # avol0 → lebs(avol1, m0, m) = lebs(avol0, m0, m) ⊦ lebs(avol1, m0, m +1) = lebs(avol0, m0, m +1)

Rule argument

indvar: m1

Additional information

Used simplifier rules: lebs-base: ⊦ lebs(avol, n, 0) = mkbuf(0);%nat freely generated by 0, +1;;