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Proof step 72 from proof inv-allocate-gnd (previous step)

# lpt0 = # avol0, # lpt = # avol0, lpt[n0] = mklp(0, m3, LP_FREE, m2), err = err0, err = ESUCCESS, err1 = err, freelist = (n0 ' + nx0).tail, keyset(gch) = gc-heap(lpt, log1), log = log1, lpt1 = lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)] [n0, lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)][n0].ref-size:= 0 ], n0 < # lpt, n0 < # lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)], n0 < # avol0, awbuf-inv(avol0[n0, mapped(mkbuf(0))], buffered(n0)), awbuf-inv(avol0, bleb), awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log1, lpt), freelist-cons(lpt, n0 ' + nx0), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), synced(avol0), synced(avol0[n0, mapped(mkbuf(0))]), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪lpt1[n0].flags := LP_GROUP_NODES; log1 := log1 + n0 '⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ log1 = log + n0 ' ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log + n0 ') ∧ bufs-log-only(buffered(n0), log + n0 ', lpt1) ∧ # lpt1 = # avol0 ∧ ¬ dups(log + n0 ') ∧ log-group-block(log + n0 ', lpt1) ∧ buf-ro-rw-mode(false, buffered(n0), lpt1, avol0[n0, mapped(mkbuf(0))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log + n0 ')), n0 ' + nx0 = [], buffered(n0) = bleb, dups(log1)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 73:
# lpt = # avol0, # lpt0 = # avol0, lpt[n0] = mklp(0, m3, LP_FREE, m2), err = ESUCCESS, err = err0, err1 = err, freelist = (n0 ' + nx0).tail, keyset(gch) = gc-heap(lpt, log1), log = log1, lpt1 = lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)] [n0, lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)][n0].ref-size:= 0 ], n0 < # lpt1, n0 < # avol0, n0 < # lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)], n0 < # lpt, awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), awbuf-inv(avol0, bleb), awbuf-inv(avol0[n0, mapped(mkbuf(0))], buffered(n0)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log1, lpt), freelist-cons(lpt, n0 ' + nx0), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), synced(avol0[n0, mapped(mkbuf(0))]), synced(avol0), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪log1 := log1 + n0 '⟫ ( lpt-free-unref(lpt1[n0, lpt1[n0].flags:= LP_GROUP_NODES]) ∧ freelist-cons(lpt1[n0, lpt1[n0].flags:= LP_GROUP_NODES], freelist) ∧ log1 = log + n0 ' ∧ bin-heap-inv(gch, lpt1[n0, lpt1[n0].flags:= LP_GROUP_NODES]) ∧ keyset(gch) = gc-heap(lpt1[n0, lpt1[n0].flags:= LP_GROUP_NODES], log + n0 ') ∧ bufs-log-only(buffered(n0), log + n0 ', lpt1[n0, lpt1[n0].flags:= LP_GROUP_NODES]) ∧ # lpt1[n0, lpt1[n0].flags:= LP_GROUP_NODES] = # avol0 ∧ ¬ dups(log + n0 ') ∧ log-group-block(log + n0 ', lpt1[n0, lpt1[n0].flags:= LP_GROUP_NODES]) ∧ buf-ro-rw-mode(false, buffered(n0), lpt1[n0, lpt1[n0].flags:= LP_GROUP_NODES], avol0[n0, mapped(mkbuf(0))]) ∧ lpt-leb-size(lpt1[n0, lpt1[n0].flags:= LP_GROUP_NODES]) ∧ lpt-ram-flash(lpt1[n0, lpt1[n0].flags:= LP_GROUP_NODES], lpt0, log + n0 ')), n0 ' + nx0 = [], buffered(n0) = bleb, dups(log1)

Rule argument

Additional information

Used simplifier rules: ⊦ n ' + nx ≠ []; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ # lpt[n, lp] = # lpt; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)% ⊦ mklp(m, m0, lpf, m1).ref-size:= m2 = mklp(m2, m0, lpf, m1); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # lpt ⊦ lpt[m, lp][m, lp0] = lpt[m, lp0]; (s)