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Proof step 8 from proof abs-idset-fwd (previous step)

# vols[v] = # avols[v], avols[v][m].data = apebs0[vols[v][m].pnum].data, apebs1[vols[v][m].pnum] = mkpeb(aehdr, avhdr, buf, m0, boolvar), avols[v][m].mapped?, m < # avols[v], id(apebs1, apebs0, mapped-pebs(vols)), valid-ebatbl(apebs0, wlar, vols, n0), v ∈ avols, v ∈ vols, apebs0[vols[v][m].pnum].fill ≤ avols[v][m].fill, avols[v][m] = erased → ¬ v × m ∈ q ⊦ vols[v][m] = unmapped, avols[v][m].data = buf ∧ m0 ≤ avols[v][m].fill

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
# vols[v] = # avols[v], apebs1[vols[v][m].pnum] = mkpeb(aehdr, avhdr, buf, m0, boolvar), avols[v][m] = mapped(buf0, m1), buf0 = apebs0[vols[v][m].pnum].data, avols[v][m].mapped?, m < # avols[v], id(apebs1, apebs0, mapped-pebs(vols)), valid-ebatbl(apebs0, wlar, vols, n0), v ∈ vols, v ∈ avols, apebs0[vols[v][m].pnum].fill ≤ m1, avols[v][m] = erased → ¬ v × m ∈ q ⊦ vols[v][m] = unmapped, buf0 = buf ∧ m0 ≤ m1

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][m], buf0, m1]

Additional information

Used simplifier rules: ⊦ leb.mapped? → (buf = leb.data ∧ m = leb.fill ↔ leb = mapped(buf, m)); (elim) Used terms: avols[v][m], buf0, m1