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Proof step 94 from proof inv-allocate-gnd (previous step)

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

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 95:
# lpt1 = # avol0, # lpt0 = # avol0, lpt1[n0] = mklp(0, m3, LP_FREE, m2), err = err0, freelist = (n0 ' + nx0).tail, keyset(gch) = gc-heap(lpt1, log1), log = log1, n0 < # avol0, awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, bleb, lpt1, avol0), bufs-log-only(bleb, log1, lpt1), freelist-cons(lpt1, n0 ' + nx0), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), synced(avol0[n0, mapped(mkbuf(0))]), synced(avol0), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪err1 := err; if err1 ≠ ESUCCESS then freelist := n0 ' + freelist; lpt1 := lpt1[n0, mklp(lpt1[n0].ref-size, 0, lpt1[n0].flags, lpt1[n0].gcheapidx)] [n0, lpt1[n0, mklp(lpt1[n0].ref-size, 0, lpt1[n0].flags, lpt1[n0].gcheapidx)][n0].ref-size:= 0 ]; if err1 = ESUCCESS then {lpt1[n0].flags := LP_GROUP_NODES; log1 := log1 + n0 '}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ log1 = log ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log) ∧ bufs-log-only(bleb, log, lpt1) ∧ # lpt1 = # avol0 ∧ ¬ dups(log) ∧ log-group-block(log, lpt1) ∧ buf-ro-rw-mode(false, bleb, lpt1, avol0[n0, mapped(mkbuf(0))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log)), n0 ' + nx0 = [], buffered(n0) = bleb, err = ESUCCESS, dups(log1)

Rule argument

Additional information

Used simplifier rules: ⊦ nx + nx0 = [] ↔ nx = [] ∧ nx0 = []; (as)% ⊦ n ' ≠ []; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]