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Proof step 16 from proof absexpt-vols-write (previous step)

m < # vols[v], v ∈ vols, ∀ v1. (v1 ∈ vols ↔ v1 ∈ avols) ∧ ( v1 ∈ vols → # vols[v1] = # avols[v1] ∧ (∀ m1. (v1 ≠ v ∨ m1 ≠ m) ∧ m1 < # vols[v1] → (vols[v1][m1] = unmapped → ¬ avols[v1][m1].mapped?) ∧ ( vols[v1][m1] ≠ unmapped → avols[v1][m1].mapped? ∧ avols[v1][m1].data = apebs[vols[v1][m1].pnum].data ∧ apebs[vols[v1][m1].pnum].fill ≤ avols[v1][m1].fill) ∧ (avols[v1][m1] = erased → ¬ v1 × m1 ∈ q))) ⊦ (v0 ∈ vols[v, vols[v][m, ebae]] ↔ v0 ∈ avols) ∧ ( v0 ∈ vols[v, vols[v][m, ebae]] → # vols[v, vols[v][m, ebae]][v0] = # avols[v0] ∧ ( (v0 ≠ v ∨ m0 ≠ m) ∧ m0 < # vols[v, vols[v][m, ebae]][v0] → (vols[v, vols[v][m, ebae]][v0][m0] = unmapped → ¬ avols[v0][m0].mapped?) ∧ ( vols[v, vols[v][m, ebae]][v0][m0] ≠ unmapped → avols[v0][m0].mapped? ∧ avols[v0][m0].data = apebs[vols[v, vols[v][m, ebae]][v0][m0].pnum].data ∧ apebs[vols[v, vols[v][m, ebae]][v0][m0].pnum].fill ≤ avols[v0][m0].fill) ∧ (avols[v0][m0] = erased → ¬ v0 × m0 ∈ q)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
apebs[vols[v, vols[v][m, ebae]][v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m2, boolvar), m < # vols[v], v ∈ vols, ∀ v1. (v1 ∈ vols ↔ v1 ∈ avols) ∧ ( v1 ∈ vols → # vols[v1] = # avols[v1] ∧ (∀ m1. (v1 ≠ v ∨ m1 ≠ m) ∧ m1 < # vols[v1] → (vols[v1][m1] = unmapped → ¬ avols[v1][m1].mapped?) ∧ ( vols[v1][m1] ≠ unmapped → avols[v1][m1].mapped? ∧ avols[v1][m1].data = apebs[vols[v1][m1].pnum].data ∧ apebs[vols[v1][m1].pnum].fill ≤ avols[v1][m1].fill) ∧ (avols[v1][m1] = erased → ¬ v1 × m1 ∈ q))) ⊦ (v0 ∈ vols[v, vols[v][m, ebae]] ↔ v0 ∈ avols) ∧ ( v0 ∈ vols[v, vols[v][m, ebae]] → # vols[v, vols[v][m, ebae]][v0] = # avols[v0] ∧ ( (v0 ≠ v ∨ m0 ≠ m) ∧ m0 < # vols[v, vols[v][m, ebae]][v0] → (vols[v, vols[v][m, ebae]][v0][m0] = unmapped → ¬ avols[v0][m0].mapped?) ∧ (vols[v, vols[v][m, ebae]][v0][m0] ≠ unmapped → avols[v0][m0].mapped? ∧ avols[v0][m0].data = buf ∧ m2 ≤ avols[v0][m0].fill) ∧ (avols[v0][m0] = erased → ¬ v0 × m0 ∈ q)))

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[vols[v, vols[v][m, ebae]][v0][m0].pnum], aehdr, avhdr, buf, m2, boolvar]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[vols[v, vols[v][m, ebae]][v0][m0].pnum], aehdr, avhdr, buf, m2, boolvar