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Proof step 5 from proof ebm-cons-write (previous step)

leb.mapped?, m < # avols[v], v ∈ avols, avols[v][m].mapped? → # avols[v][m].data = LEB_SIZE ∧ avols[v][m].fill ≤ LEB_SIZE ∧ is-aligned(avols[v][m].fill, EB_PAGE_SIZE) ∧ range=(avols[v][m].data, avols[v][m].fill, emptyleb, 0, LEB_SIZE - avols[v][m].fill), ∀ v0. v0 ∈ avols[v, avols[v][m, leb]] → (∀ m0. m0 < # avols[v, avols[v][m, leb]][v0] → avols[v, avols[v][m, leb]][v0][m0].mapped? → # avols[v, avols[v][m, leb]][v0][m0].data = LEB_SIZE ∧ avols[v, avols[v][m, leb]][v0][m0].fill ≤ LEB_SIZE ∧ is-aligned(avols[v, avols[v][m, leb]][v0][m0].fill, EB_PAGE_SIZE) ∧ range= (avols[v, avols[v][m, leb]][v0][m0].data, avols[v, avols[v][m, leb]][v0][m0].fill, emptyleb, 0, LEB_SIZE - avols[v, avols[v][m, leb]][v0][m0].fill)), ∀ v0. v0 ∈ avols → (∀ m0. m0 < # avols[v0] → avols[v0][m0].mapped? → # avols[v0][m0].data = LEB_SIZE ∧ avols[v0][m0].fill ≤ LEB_SIZE ∧ is-aligned(avols[v0][m0].fill, EB_PAGE_SIZE) ∧ range=(avols[v0][m0].data, avols[v0][m0].fill, emptyleb, 0, LEB_SIZE - avols[v0][m0].fill)) ⊦ # leb.data = LEB_SIZE ∧ leb.fill ≤ LEB_SIZE ∧ is-aligned(leb.fill, EB_PAGE_SIZE) ∧ range=(leb.data, leb.fill, emptyleb, 0, LEB_SIZE - leb.fill)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
leb = mapped(buf, m1), leb.mapped?, m < # avols[v], v ∈ avols, avols[v][m].mapped? → # avols[v][m].data = LEB_SIZE ∧ avols[v][m].fill ≤ LEB_SIZE ∧ is-aligned(avols[v][m].fill, EB_PAGE_SIZE) ∧ range=(avols[v][m].data, avols[v][m].fill, emptyleb, 0, LEB_SIZE - avols[v][m].fill), ∀ v0. v0 ∈ avols → (∀ m0. m0 < # avols[v0] → avols[v0][m0].mapped? → # avols[v0][m0].data = LEB_SIZE ∧ avols[v0][m0].fill ≤ LEB_SIZE ∧ is-aligned(avols[v0][m0].fill, EB_PAGE_SIZE) ∧ range=(avols[v0][m0].data, avols[v0][m0].fill, emptyleb, 0, LEB_SIZE - avols[v0][m0].fill)), ∀ v0. v0 ∈ avols[v, avols[v][m, leb]] → (∀ m0. m0 < # avols[v, avols[v][m, leb]][v0] → avols[v, avols[v][m, leb]][v0][m0].mapped? → # avols[v, avols[v][m, leb]][v0][m0].data = LEB_SIZE ∧ avols[v, avols[v][m, leb]][v0][m0].fill ≤ LEB_SIZE ∧ is-aligned(avols[v, avols[v][m, leb]][v0][m0].fill, EB_PAGE_SIZE) ∧ range= (avols[v, avols[v][m, leb]][v0][m0].data, avols[v, avols[v][m, leb]][v0][m0].fill, emptyleb, 0, LEB_SIZE - avols[v, avols[v][m, leb]][v0][m0].fill)) ⊦ # buf = LEB_SIZE ∧ m1 ≤ LEB_SIZE ∧ is-aligned(m1, EB_PAGE_SIZE) ∧ range=(buf, m1, emptyleb, 0, LEB_SIZE - m1)

Rule argument

spec: leb name: elim seq: ⊦ leb.mapped? → (buf = leb.data ∧ m = leb.fill ↔ leb = mapped(buf, m)) subst: [leb, buf, m] → [leb, buf, m1]

Additional information

Used simplifier rules: ⊦ leb.mapped? → (buf = leb.data ∧ m = leb.fill ↔ leb = mapped(buf, m)); (elim) Used terms: leb, buf, m1