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Proof step 34 from proof inv-add-ind (previous step)

# lpt0 = # avol, # lpt1 = # avol, # buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, avol[n] = mapped(buf0), lpt1[n] = mklp(m1, # buf0, LP_INDEX_NODES, m2), ¬ isbuf1, keyset(gch) = gc-heap(lpt1, log0), n < # avol, abs-node(buf1, ind), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), 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), # buf0 + # buf1 ≤ LEB_SIZE ⊦ ⟪awbuf_write_buf#(# buf1, buf1, adr0, m0, log0, lpt0, ns, buffered(n); avol, isbuf1; err); if err = ESUCCESS then {adr := @(buffered(n).leb, lpt1[buffered(n).leb].size, # buf1); lpt1[buffered(n).leb] := mklp (lpt1[buffered(n).leb].ref-size, lpt1[buffered(n).leb].size + # buf1, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx)} else lpt1[buffered(n).leb] := mklp(lpt1[buffered(n).leb].ref-size, LEB_SIZE, lpt1[buffered(n).leb].flags, lpt1[buffered(n).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(n), log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, buffered(n), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, buffered(n)) ∧ # lpt0 = # avol)

User applied rule insert program lemma

And obtained the following new goals

Proof step 35:
awbuf-inv(avol, bleb), # lpt = # avol, bleb ≠ nobuffer, # avol[bleb.leb].data + n ≤ LEB_SIZE, n ≤ # buf ⊦ ⟪awbuf_write_buf#(n, buf, adr, m, nx, lpt, ns, bleb; avol, isbuf; err)⟫ (awbuf-inv(avol, bleb) ∧ # lpt = # avol)
Proof step 36:
# buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt1 = # avol, # lpt0 = # avol, lpt1[n] = mklp(m1, # buf0, LP_INDEX_NODES, m2), avol[n] = mapped(buf0), adr1 = adr0, bleb0 = buffered(n), buf2 = buf1, ¬ isbuf1, keyset(gch) = gc-heap(lpt1, log0), lpt2 = lpt0, m3 = m0, n0 = # buf1, ns0 = ns, nx0 = log0, n < # avol, abs-node(buf1, ind), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), 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), # buf0 + # buf1 ≤ LEB_SIZE, # avol[buffered(n).leb].data + # buf1 ≤ LEB_SIZE, # buf1 ≤ # buf1 ⊦ [awbuf_write_buf#(# buf1, buf1, adr0, m0, log0, lpt0, ns, buffered(n); avol, isbuf1; err)] ( awbuf-inv(avol, bleb0) ∧ # lpt2 = # avol → ⟪if err = ESUCCESS then {adr := @(buffered(n).leb, lpt1[buffered(n).leb].size, # buf1); lpt1[buffered(n).leb] := mklp (lpt1[buffered(n).leb].ref-size, lpt1[buffered(n).leb].size + # buf1, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx)} else lpt1[buffered(n).leb] := mklp(lpt1[buffered(n).leb].ref-size, LEB_SIZE, lpt1[buffered(n).leb].flags, lpt1[buffered(n).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(n), log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, buffered(n), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, buffered(n)) ∧ # lpt0 = # avol)), buffered(n) = nobuffer

Rule argument

spec: awbuf-asm name: inv-write-buf seq: awbuf-inv(avol, bleb), # lpt = # avol, bleb ≠ nobuffer, # avol[bleb.leb].data + n ≤ LEB_SIZE, n ≤ # buf ⊦ ⟪awbuf_write_buf# (n, buf, adr, m, nx, lpt, ns, bleb; avol, isbuf; err)⟫ (awbuf-inv(avol, bleb) ∧ # lpt = # avol) subst: [bleb, ns, lpt, nx, m, adr, buf, n, isbuf, avol, err] → [buffered(n), ns, lpt0, log0, m0, adr0, buf1, # buf1, isbuf1, avol, err] flags: <all paths>

Additional information

Used simplifier rules: ⊦ nobuffer ≠ buffered(m); (s)% ⊦ buffered(m).leb = m; (s)% ⊦ m ≤ m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ mapped(buf).data = buf; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic