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Proof step 14 from proof abs-erase-emptyq (previous step)

# vols[v] = # avols[v], apebs[vols[v][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # avols[v], m < # avols[v], v ∈ vols, v ∈ avols, ∀ m. m < # avols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q) ⊦ m0 = m, (vols[v][m0] = unmapped → ¬ avols[v][m0].mapped?) ∧ (vols[v][m0] ≠ unmapped → avols[v][m0].mapped? ∧ avols[v][m0].data = buf ∧ m1 ≤ avols[v][m0].fill)

User applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: m0 abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s) Used terms: m0