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Proof step 37 from proof recovery (previous step)

# vols[v] = # vols0[v], # wlar = # wlar0, # apebs0 = # wlar0, # avols0[v] = # vols0[v], apebs0[vols[v][m].pnum] = mkpeb(aehdr, avhdr, buf, m0, boolvar), m < # vols0[v], bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols0), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-ebatbl(apebs0, wlar, vols, vtblpnum), valid-eraseq(apebs0, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, vtblpnum0), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-vtbl(apebs0, vols, wlar, vtblpnum), valid-wl(apebs0, wlar0), valid-wl(apebs0, wlar), v ∈ avols0, v ∈ vols, v ∈ vols0, q0.lebrefs ⊆ q.lebrefs, vols0⌈vols, q⌉, avols0[v][m] = erased → ¬ v × m ∈ q, vols[v][m] ≠ unmapped → avols0[v][m].mapped? ∧ avols0[v][m].data = buf ∧ m0 ≤ avols0[v][m].fill, vols[v][m] = unmapped → ¬ avols0[v][m].mapped?, vols[v][m] ≠ unmapped → vols[v][m] = vols0[v][m] ⊦ avols0[v][m] = unmapped, VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols0, (avols0[v][m] = erased → absf(v, avols0[v], apebs0, vols0[v], q0, # vols0[v])[m] = erased) ∧ (avols0[v][m].mapped? → absf(v, avols0[v], apebs0, vols0[v], q0, # vols0[v])[m] = avols0[v][m])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ n < m ∧ m ≤ # ebatbl → absf(v, evol, apebs, ebatbl, q, m)[n] = (ebatbl[n] = unmapped ⊃ (v × n ∈ q.lebrefs ⊃ unmapped;erased) ;mapped(apebs[ebatbl[n].pnum].data, (evol[n].mapped? ⊃ evol[n].fill;apebs[ebatbl[n].pnum].fill)) )
Proof step 39:
# avols0[v] = # vols0[v], # apebs0 = # wlar0, # wlar = # wlar0, # vols[v] = # vols0[v], apebs0[vols[v][m].pnum] = mkpeb(aehdr, avhdr, buf, m0, boolvar), m < # vols0[v], bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), ebm-cons(avols0), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-global-sqn(apebs0, vtblpnum0), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar0), v ∈ vols0, v ∈ vols, v ∈ avols0, # vols0[v] ≤ # vols0[v], q0.lebrefs ⊆ q.lebrefs, vols0⌈vols, q⌉, vols[v][m] ≠ unmapped → vols[v][m] = vols0[v][m], vols[v][m] = unmapped → ¬ avols0[v][m].mapped?, vols[v][m] ≠ unmapped → avols0[v][m].mapped? ∧ avols0[v][m].data = buf ∧ m0 ≤ avols0[v][m].fill, avols0[v][m] = erased → ¬ v × m ∈ q ⊦ avols0[v][m] = unmapped, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols, ( avols0[v][m] = erased → (vols0[v][m] = unmapped ⊃ (v × m ∈ q0.lebrefs ⊃ unmapped;erased) ;mapped(apebs0[vols0[v][m].pnum].data, (avols0[v][m].mapped? ⊃ avols0[v][m].fill;apebs0[vols0[v][m].pnum].fill)) ) = erased) ∧ ( avols0[v][m].mapped? → (vols0[v][m] = unmapped ⊃ (v × m ∈ q0.lebrefs ⊃ unmapped;erased) ;mapped(apebs0[vols0[v][m].pnum].data, (avols0[v][m].mapped? ⊃ avols0[v][m].fill;apebs0[vols0[v][m].pnum].fill)) ) = avols0[v][m])

Rule argument

spec: ubi-abs name: absf-at seq: ⊦ n < m ∧ m ≤ # ebatbl → absf(v, evol, apebs, ebatbl, q, m)[n] = (ebatbl[n] = unmapped ⊃ (v × n ∈ q.lebrefs ⊃ unmapped;erased) ;mapped (apebs[ebatbl[n].pnum].data, (evol[n].mapped? ⊃ evol[n].fill ;apebs[ebatbl[n].pnum].fill )) ) subst: [n, m, q, ebatbl, apebs, evol, v] → [m, # vols0[v], q0, vols0[v], apebs0, avols0[v], v] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ m; (s) Used terms: m, # vols0[v], q0, vols0[v], apebs0, avols0[v], v