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Proof step 66 from proof inv-add-gnds (previous step)

# gndx = # lax, # buf0 = gndx.flashsize, # lpt1 = # avol, # lpt0 = # avol, avol[n1] = mapped(buf1), lpt1[n1] = mklp(m4, # buf1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, log0), gndx ≠ [], n ≠ 0, n < gndx.flashsize, n1 < # avol, abs-nodes(buf0, # buf1, gndx, lax, false), awbuf-inv(avol[n1, mapped(buf1 + subarray(buf0, 0, n))], buffered(n1)), awbuf-inv(avol, buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol), bufs-log-only(buffered(n1), log0, lpt1), freelist-cons(lpt1, freelist), is-aligned(# buf1 + n, EB_PAGE_SIZE), log-group-block(log0, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), n1 ∈ log0, # buf1 + gndx.flashsize ≤ LEB_SIZE, ⌊err0⌋ , ¬ dups(log0) ⊦ ⟪lpt1[buffered(n1).leb] := mklp(lpt1[buffered(n1).leb].ref-size, LEB_SIZE, lpt1[buffered(n1).leb].flags, lpt1[buffered(n1).leb].gcheapidx)⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(buffered(n1), log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(true, buffered(n1), lpt1, avol[n1, mapped(avol[n1].data + subarray(buf0, 0, n))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0))

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ buffered(m).leb = m; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s)%⊦ lpt-free-unref(lpt) → ( lpt-free-unref(lpt[n, lp]) ↔ n < # lpt ∧ lp.flags = LP_FREE → lp.ref-size = 0); (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ mklp(n2, n3, lpf, m).gcheapidx = m; (s)%lpt[n].flags = lp.flags ⊦ bufs-log-only(bleb, nx, lpt) → bufs-log-only(bleb, nx, lpt[n, lp]); (s)% ⊦ # lpt[n, lp] = # lpt; (s)%⊦ buf-ro-rw-mode (true, buffered(n), lpt[n, mklp(m0, LEB_SIZE, lpf, m1)], avol) ↔ n < # lpt; (s)%⊦ lpt-leb-size(lpt) → (lpt-leb-size(lpt[n, lp]) ↔ # lpt ≤ n ∨ lp.size ≤ LEB_SIZE); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ m ≤ m; (s)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)%⊦ freelist-cons(lpt, freelist) ∧ lpt[n] = mklp(m0, m1, lpf, m2) → freelist-cons(lpt[n, mklp(n0, n1, lpf, n2)], freelist); (s)%n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → ( bin-heap-inv(gch, lpt[n, mklp(n0, n1, lpf1, m2)]) ↔ bin-heap-inv(gch, lpt)); (s)%n < # lpt ⊦ lpt[n] = mklp(m0, m1, LP_GROUP_NODES, m2) → gc-heap(lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)], nx) = gc-heap(lpt, nx); (s)%n < # lpt ⊦ lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ log-group-block(nx, lpt) → log-group-block(nx, lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)]); (s)%n < # lpt ⊦ bufs-log-only(buffered(n), nx, lpt) ∧ lpt-ram-flash(lpt, lpt0, nx) ∧ lpt[n] = mklp(n0, n1, lpf, n2) → lpt-ram-flash(lpt[n, mklp(m0, m1, lpf, m2)], lpt0, nx); (ss)