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Proof step 6 from proof abs-idset-fwd (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 7:
# vols[v] = # avols[v], apebs1[vols[v][m].pnum] = mkpeb(aehdr, avhdr, buf, m0, boolvar), m < # avols[v], id(apebs1, apebs0, mapped-pebs(vols)), valid-ebatbl(apebs0, wlar, vols, n0), v ∈ vols, v ∈ avols, m < # avols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs0[vols[v][m].pnum].data ∧ apebs0[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q) ⊦ (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = buf ∧ m0 ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q)

Rule argument

pos: left 8 terms: m abort: F discard: T computed: T

Additional information

Used terms: m