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Proof step 133 from proof refine-commit (previous step)

# lpt0 = # avol0, # lpt2 = # avol0, # avol = # avol0, # lpt = # avol0, # lpt1 = # avol0, istore2[n] = indexblock(indx0, lax1, m4), remove-refsize0(gstore2)[n] = groupblock(gndx, lax0, m0), remove-refsize0(istore2)[n] = indexblock(indx, lax, m), lpt2[n] = mklp(m1, m2, lpf, m3), keyset(gch) = gc-heap(lpt2, log1), keyset(gch0) = gc-heap(lpt2, []), keyset(gch1) = gc-heap(cleanup-lpt(lpt), []), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, dom remove-refsize0(gstore2) ∩ ginval = ∅, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol0, n < # avol0, abs-gstore(avol, lpt2, gstore2, ginval), abs-istore(avol, lpt2, istore2), avol-cleanup-lpt-unchanged(avol, avol0, lpt), awbuf-inv(avol, bleb0), awbuf-inv(avol, nobuffer), awbuf-inv(avol0, nobuffer), bin-heap-inv(gch, lpt2), bin-heap-inv(gch0, lpt), bin-heap-inv(gch1, lpt1), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), freelist-cons(lpt2, freelist), freelist-cons(cleanup-lpt(lpt), freelist0), id-idx(lpt2, lpt), id-idx(cleanup-lpt(lpt), lpt1), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-leb-size(cleanup-lpt(lpt)), lpt-ram-flash(lpt2, lpt0, log1), lpt-ram-flash(lpt1, lpt2, []), synced(avol), synced(avol0), istore1 ⊑ istore2, n ∈ log1 → lpf = LP_GROUP_NODES, pstate ≠ unbuffered → bleb0 = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate = unbuffered → bleb0 = nobuffer, ∀ n. n < # avol0 → (n ∈ istore1 ↔ lpt0[n].flags = LP_INDEX_NODES ∧ lpt0[n].ref-size ≠ 0) ∧ (n ∈ gstore1 ↔ lpt0[n].flags = LP_GROUP_NODES ∧ lpt0[n].ref-size ≠ 0) ∧ (n ∈ istore1 → lpt0[n].ref-size = istore1[n].ref-size) ∧ (n ∈ gstore1 → lpt0[n].ref-size = gstore1[n].ref-size) ∧ (lpt0[n].flags = LP_FREE → lpt0[n].ref-size = 0) ⊦ pstate = readonly, dups(log1), (n ∈ istore2 ∧ m4 ≠ 0 ↔ lpf = LP_INDEX_NODES ∧ m1 ≠ 0) ∧ (n ∈ gstore2 ∧ gstore2[n].ref-size ≠ 0 ↔ lpf = LP_GROUP_NODES ∧ m1 ≠ 0) ∧ (n ∈ istore2 ∧ m4 ≠ 0 → m1 = m) ∧ (n ∈ gstore2 ∧ gstore2[n].ref-size ≠ 0 → m1 = m0) ∧ (lpf = LP_FREE → m1 = 0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 134:
# lpt1 = # avol0, # lpt = # avol0, # avol = # avol0, # lpt2 = # avol0, # lpt0 = # avol0, lpt2[n] = mklp(m1, m2, lpf, m3), remove-refsize0(istore2)[n] = indexblock(indx, lax, m), remove-refsize0(gstore2)[n] = groupblock(gndx, lax0, m0), istore2[n] = indexblock(indx0, lax1, m4), gstore2[n] = groupblock(gndx0, lax2, m5), keyset(gch1) = gc-heap(cleanup-lpt(lpt), []), keyset(gch0) = gc-heap(lpt2, []), keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom remove-refsize0(gstore2) ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, n < # avol0, ginval < # avol0, abs-gstore(avol, lpt2, gstore2, ginval), abs-istore(avol, lpt2, istore2), avol-cleanup-lpt-unchanged(avol, avol0, lpt), awbuf-inv(avol0, nobuffer), awbuf-inv(avol, nobuffer), awbuf-inv(avol, bleb0), bin-heap-inv(gch1, lpt1), bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), freelist-cons(cleanup-lpt(lpt), freelist0), freelist-cons(lpt2, freelist), id-idx(cleanup-lpt(lpt), lpt1), id-idx(lpt2, lpt), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(cleanup-lpt(lpt)), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt1, lpt2, []), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), synced(avol), istore1 ⊑ istore2, pstate = unbuffered → bleb0 = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, pstate ≠ unbuffered → bleb0 = buffered(pstate.lnum), n ∈ log1 → lpf = LP_GROUP_NODES, ∀ n. n < # avol0 → (n ∈ istore1 ↔ lpt0[n].flags = LP_INDEX_NODES ∧ lpt0[n].ref-size ≠ 0) ∧ (n ∈ gstore1 ↔ lpt0[n].flags = LP_GROUP_NODES ∧ lpt0[n].ref-size ≠ 0) ∧ (n ∈ istore1 → lpt0[n].ref-size = istore1[n].ref-size) ∧ (n ∈ gstore1 → lpt0[n].ref-size = gstore1[n].ref-size) ∧ (lpt0[n].flags = LP_FREE → lpt0[n].ref-size = 0) ⊦ pstate = readonly, dups(log1), (n ∈ istore2 ∧ m4 ≠ 0 ↔ lpf = LP_INDEX_NODES ∧ m1 ≠ 0) ∧ (n ∈ gstore2 ∧ m5 ≠ 0 ↔ lpf = LP_GROUP_NODES ∧ m1 ≠ 0) ∧ (n ∈ istore2 ∧ m4 ≠ 0 → m1 = m) ∧ (n ∈ gstore2 ∧ m5 ≠ 0 → m1 = m0) ∧ (lpf = LP_FREE → m1 = 0)

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore2[n], gndx0, lax2, m5]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore2[n], gndx0, lax2, m5