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Proof step 15 from proof crash-neutral-write (previous step)

avols[v][m2].mapped?, m2 < # avols[v], ebm-cons(avols0), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), v ∈ avols, n + n2 ≤ # buf, m1 + n ≤ LEB_SIZE, avols[v][m2].fill ≤ m1, avols ⊆ avols0 ⊦ (¬ n0 < n ∨ ¬ is-aligned(n0, EB_PAGE_SIZE)) ∧ ⟨skip⟩ true, ∃ n1. n1 < n ∧ is-aligned(n1, EB_PAGE_SIZE) ∧ ⟨if n1 ≠ 0 then avols[v][m2] := mapped(subarray(avols[v][m2].data, 0, m1) + subarray(buf, n2, n1) + mkempbuf(LEB_SIZE - m1 - n1), m1 + n1)⟩ (avols ⊆ avols0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
avols[v][m2] = mapped(buf0, m), avols[v][m2].mapped?, m2 < # avols[v], ebm-cons(avols), ebm-cons(avols0), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), v ∈ avols, m ≤ m1, m1 + n ≤ LEB_SIZE, n + n2 ≤ # buf, avols ⊆ avols0 ⊦ (¬ n0 < n ∨ ¬ is-aligned(n0, EB_PAGE_SIZE)) ∧ ⟨skip⟩ true, ∃ n1. n1 < n ∧ is-aligned(n1, EB_PAGE_SIZE) ∧ ⟨if n1 ≠ 0 then avols[v][m2] := mapped(subarray(avols[v][m2].data, 0, m1) + subarray(buf, n2, n1) + mkempbuf(LEB_SIZE - m1 - n1), m1 + n1)⟩ (avols ⊆ avols0)

Rule argument

spec: leb name: elim seq: ⊦ leb.mapped? → (buf = leb.data ∧ m = leb.fill ↔ leb = mapped(buf, m)) subst: [leb, buf, m] → [avols[v][m2], buf0, m]

Additional information

Used simplifier rules: ⊦ leb.mapped? → (buf = leb.data ∧ m = leb.fill ↔ leb = mapped(buf, m)); (elim) Used terms: avols[v][m2], buf0, m