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Proof step 8 from proof down-written-not-down-before (previous step)

# avol1 = # avol0, n < # avol0, n0 < # avol0, avol0[n].mapped? → avol1[n] = mapped(subarray(avol0[n].data, 0, align↓(# avol0[n].data, EB_PAGE_SIZE))), ¬ avol0[n].mapped? ∧ avol1[n].mapped? → # avol1[n].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n].data, EB_PAGE_SIZE), avol0[n, aleb][n0].mapped? → avol1[n0] = mapped(subarray(avol0[n, aleb][n0].data, 0, align↓(# avol0[n, aleb][n0].data, EB_PAGE_SIZE))), ¬ avol0[n, aleb][n0].mapped? ∧ avol1[n0].mapped? → # avol1[n0].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n0].data, EB_PAGE_SIZE) ⊦ (avol0[n0].mapped? → avol1[n0] = mapped(subarray(avol0[n0].data, 0, align↓(# avol0[n0].data, EB_PAGE_SIZE)))) ∧ (¬ avol0[n0].mapped? ∧ avol1[n0].mapped? → # avol1[n0].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n0].data, EB_PAGE_SIZE))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array, inst: avolume name: Put-other seq: ⊦ m ≠ n → avol[n, aleb][m] = avol[m] subst: [m, aleb, n, avol] → [n0, aleb, n, avol0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < # avol → avol[m, aleb][m] = aleb; (s) Used terms: n0, aleb, n, avol0