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Proof step 2 from proof ebm-vol-inv-write (previous step)

n < # avol, ebm-vol-inv(avol) ⊦ ebm-vol-inv(avol[n, aleb]) ↔ (avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE)) → aleb.mapped? → # aleb.data ≤ LEB_SIZE ∧ is-aligned(# aleb.data, EB_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < # avol, ∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE) ⊦ (∀ n0. n0 < # avol ∧ avol[n, aleb][n0].mapped? → # avol[n, aleb][n0].data ≤ LEB_SIZE ∧ is-aligned(# avol[n, aleb][n0].data, EB_PAGE_SIZE)) ↔ (avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE)) → aleb.mapped? → # aleb.data ≤ LEB_SIZE ∧ is-aligned(# aleb.data, EB_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ebm-vol-inv: ⊦ ebm-vol-inv(avol) ↔ (∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE));% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # avol[n, aleb] = # avol; (s)