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Proof step 28 from proof inv-set-gblock-refsize (previous step)

# lpt1 = # avol, lpt1[m] = mklp(m0, m1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, log), lpt = lpt1[m, lpt1[m].ref-size:= n], m < # lpt1, m < # avol, bin-heap-inv(gch, lpt1), buf-ro-rw-mode(isbuf, bleb, lpt1, avol), bufs-log-only(bleb, log, lpt1), freelist-cons(lpt1, freelist), log-group-block(log, lpt1), lpt-free-unref(lpt1), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log), m ∈ log ⊦ ⟪skip⟫ ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log) ∧ bufs-log-only(bleb, log, lpt) ∧ # lpt = # avol ∧ log-group-block(log, lpt) ∧ buf-ro-rw-mode(isbuf, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log)), dups(log)

Heuristic symbolic execution applied rule skip right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ lpt-free-unref(lpt) → ( lpt-free-unref(lpt[n, lp]) ↔ n < # lpt ∧ lp.flags = LP_FREE → lp.ref-size = 0); (s)% ⊦ (lp.ref-size:= m).flags = lp.flags; (s)% ⊦ (lp.ref-size:= m).ref-size = m; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ mklp(m, m0, lpf, m1).ref-size:= m2 = mklp(m2, m0, lpf, m1); (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)%⊦ lpt-leb-size(lpt) → (lpt-leb-size(lpt[n, lp]) ↔ # lpt ≤ n ∨ lp.size ≤ LEB_SIZE); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ (lp.ref-size:= m).size = lp.size; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ 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)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%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(n0, n1, LP_GROUP_NODES, n2) ∧ n ∈ nx → gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], 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)%⊦ lpt[n] = mklp(m0, n1, lpf0, m1) → ( buf-ro-rw-mode (boolvar, bleb, lpt[n, mklp(n0, n1, lpf1, n2)], avol) ↔ buf-ro-rw-mode(boolvar, bleb, lpt, avol)); (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%n < # lpt ⊦ lpt[n] = mklp(n0, n1, lpf, n2) ∧ lpt-leb-size(lpt) → ¬ LEB_SIZE < n1; (s)%n < # lpt ⊦ lpt[n] = mklp(n0, m, lpf, n2) → ( lpt-ram-flash(lpt[n, mklp(m0, m, lpf, m2)], lpt0, nx) ↔ lpt-ram-flash(lpt, lpt0, nx)); (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)