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Proof step 63 from proof inv-allocate-ind (previous step)

# lpt2 = # avol0, # lpt0 = # avol0, lpt2[n0] = mklp(0, m3, LP_FREE, m2), err = err0, err = ESUCCESS, freelist = (n0 ' + nx0).tail, keyset(gch) = gc-heap(lpt2, log0), lpt1 = lpt2[n0, lpt2[n0, mklp(lpt2[n0].ref-size, 0, lpt2[n0].flags, lpt2[n0].gcheapidx)][n0].ref-size:= 0], n0 < # lpt1, n0 < # lpt2, n0 < # lpt2[n0, mklp(lpt2[n0].ref-size, 0, lpt2[n0].flags, lpt2[n0].gcheapidx)], n0 < # avol0, awbuf-inv(avol0[n0, mapped(mkbuf(0))], buffered(n0)), awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log0, lpt2), freelist-cons(lpt2, n0 ' + nx0), log-group-block(log0, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log0), synced(avol0), bleb ≠ nobuffer → avol0[n0, mapped(mkbuf(0))][bleb.leb].mapped? ∧ bleb.leb < # avol0 ∧ bleb.isbuf?, bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ n0 ' + nx0 = [], buffered(n0) = bleb, lpt-free-unref(lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES]) ∧ freelist-cons(lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES], freelist) ∧ bin-heap-inv(gch, lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES]) ∧ keyset(gch) = gc-heap(lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES], log0) ∧ bufs-log-only(buffered(n0), log0, lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES]) ∧ # lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES] = # avol0 ∧ log-group-block(log0, lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES]) ∧ buf-ro-rw-mode(false, buffered(n0), lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES], avol0[n0, mapped(mkbuf(0))]) ∧ lpt-leb-size(lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES]) ∧ lpt-ram-flash(lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES], lpt0, log0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
# lpt2 = # avol0, # lpt0 = # avol0, lpt2[n0] = mklp(0, m3, LP_FREE, m2), keyset(gch) = gc-heap(lpt2, log0), n0 < # avol0, awbuf-inv(avol0[n0, mapped(mkbuf(0))], buffered(n0)), awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log0, lpt2), freelist-cons(lpt2, n0 ' + nx0), log-group-block(log0, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log0), synced(avol0), bleb ≠ nobuffer → avol0[n0, mapped(mkbuf(0))][bleb.leb].mapped? ∧ bleb.leb < # avol0 ∧ bleb.isbuf?, bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE) ⊦ buffered(n0) = bleb, bufs-log-only(buffered(n0), log0, lpt2[n0, mklp(0, 0, LP_INDEX_NODES, m2)])

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(n2, n3, lpf, m).gcheapidx = m; (s)% ⊦ # avol[n, aleb] = # avol; (s)%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%n < # lpt, lpf ≠ LP_GROUP_NODES ⊦ lpt-ram-flash(lpt, lpt0, nx) → lpt-ram-flash(lpt[n, mklp(n0, n1, lpf, n2)], lpt0, nx); (ss)% ⊦ 0 ≤ m; (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)%⊦ lpt-leb-size(lpt) → (lpt-leb-size(lpt[n, lp]) ↔ # lpt ≤ n ∨ lp.size ≤ LEB_SIZE); (s)% ⊦ # mkbuf(n) = n; (s)%n < # lpt, n < # avol ⊦ buf-ro-rw-mode (false, buffered(n), lpt[n, mklp(m0, m1, lpf, m2)], avol[n, mapped(buf)]) ↔ m1 = # buf; (s)%n < # lpt, lpf ≠ LP_GROUP_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) ∧ log-group-block(nx, lpt) → log-group-block(nx, lpt[n, lp]); (s)%lpf0 ≠ LP_GROUP_NODES, lpf1 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → gc-heap(lpt[n, mklp(n0, n1, lpf1, n2)], nx) = gc-heap(lpt, nx); (s)% ⊦ LP_GROUP_NODES ≠ LP_INDEX_NODES; (s)%lpf0 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) ∧ keyset(gch) = gc-heap(lpt, nx) → ( bin-heap-inv(gch, lpt[n, mklp(n0, n1, lpf1, n2)]) ↔ bin-heap-inv(gch, lpt)); (s)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)%lpf ≠ LP_FREE ⊦ freelist-cons(lpt, n ' + freelist) → freelist-cons(lpt[n, mklp(m0, m1, lpf, m2)], freelist); (s)% ⊦ (n ' + nx).tail = nx; (s)% ⊦ LP_FREE ≠ LP_INDEX_NODES; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)%⊦ lpt-free-unref(lpt) → ( lpt-free-unref(lpt[n, lp]) ↔ n < # lpt ∧ lp.flags = LP_FREE → lp.ref-size = 0); (s)%m < # lpt ⊦ lpt[m, lp][m, lp0] = lpt[m, lp0]; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ mklp(m, m0, lpf, m1).flags:= lpf0 = mklp(m, m0, lpf0, m1); (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ mklp(m, m0, lpf, m1).ref-size:= m2 = mklp(m2, m0, lpf, m1); (s)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)% ⊦ # lpt[n, lp] = # lpt; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ n ' + nx ≠ []; (s)