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Proof step 6 from proof mapped-full-idexpt-below (previous step)

# avol1 = # avol0, n < m0, ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m] ⊦ (∀ n0. m0 ≤ n0 ∧ n0 < m0 + m1 ∧ n0 < # avol0 → avol1[n0].mapped? ∧ # avol1[n0].data = LEB_SIZE) ↔ (∀ n0. m0 ≤ n0 ∧ n0 < m0 + m1 ∧ n0 < # avol0 → avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE)

User applied rule case distinction

And obtained the following new goals

Proof step 7:
# avol1 = # avol0, n < m0, ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m], ∀ n0. m0 ≤ n0 ∧ n0 < m0 + m1 ∧ n0 < # avol0 → avol1[n0].mapped? ∧ # avol1[n0].data = LEB_SIZE ⊦ ∀ n0. m0 ≤ n0 ∧ n0 < m0 + m1 ∧ n0 < # avol0 → avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE
Proof step 11:
# avol1 = # avol0, n < m0, ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m], ∀ n0. m0 ≤ n0 ∧ n0 < m0 + m1 ∧ n0 < # avol0 → avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE ⊦ ∀ n0. m0 ≤ n0 ∧ n0 < m0 + m1 ∧ n0 < # avol0 → avol1[n0].mapped? ∧ # avol1[n0].data = LEB_SIZE

Rule argument

pos: right 1

Proof step 6 from proof mapped-full-idexpt-below (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information