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Proof step 62 from proof inv-add-gnds (previous step)

# lpt0 = # avol, # lpt1 = # avol, # buf0 = gndx.flashsize, # gndx = # lax, # lpt0 = # avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], isbuf ↔ false, avol[n1] = mapped(buf1), lpt1[n1] = mklp(m4, # buf1, LP_GROUP_NODES, m2), err = err0, keyset(gch) = gc-heap(lpt1, log0), m = buffered(n1).leb, n0 = gndx.flashsize, buffered(n1).isbuf?, avol[m].mapped?, m < # avol, n1 < # avol, n < n0, abs-nodes(buf0, # buf1, gndx, lax, false), awbuf-inv(avol, buffered(n1)), awbuf-inv(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], 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(# avol[m].data + n, EB_PAGE_SIZE), log-group-block(log0, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log0), n1 ∈ log0, 0 + n ≤ # buf0, # buf1 + gndx.flashsize ≤ LEB_SIZE, n ≠ 0 → n < n0 → avol[m].mapped? ∧ m < # avol, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪debug#("persistence: adding group node to LEB " + buffered(n1).leb.toString + " failed"); 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[m, mapped(avol[m].data + subarray(buf0, 0, n))] ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(true, buffered(n1), lpt1, avol[m, mapped(avol[m].data + subarray(buf0, 0, n))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0)), err = ESUCCESS, gndx = [], n = 0, dups(log0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 63:
# 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) ⊦ ⟪debug#("persistence: adding group node to LEB " + buffered(n1).leb.toString + " failed"); 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))

Rule argument

Additional information

Used simplifier rules: elim-mapped: ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf));% ⊦ m < n → m ≤ n; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ gndx.flashsize = 0 ↔ gndx = []; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ buffered(m).isbuf?; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ # avol[n, aleb] = # avol; (s)% ⊦ buffered(m).leb = m; (s)