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Proof step 82 from proof refine-add-ind (previous step)

# buf1 = 2 * NODE_HEADER_SIZE + ind.alignedsize, # lpt0 = # avol, # lpt1 = # avol, avol[m0] = mapped(buf0), lpt1[m0] = mklp(m4, # buf0, LP_INDEX_NODES, m2), istore[m0] = indexblock(indx, lax, m4), ¬ isbuf2, keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, m0 < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-node(buf1, ind), awbuf-inv(avol, buffered(m0)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m0), lpt1, avol), bufs-log-only(buffered(m0), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(indexblock(indx, lax, m4)), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), 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), m0 ∈ istore, # buf0 + # buf1 ≤ LEB_SIZE, istore0 ⊑ istore, ¬ dups(log1), isbuf1 → synced(avol) ⊦ [awbuf_write_buf#(# buf1, buf1, adr0, m, log1, lpt0, ns0, buffered(m0); avol, isbuf2; err); adr := adr2; if err = ESUCCESS then {adr := @(buffered(m0).leb, lpt1[buffered(m0).leb].size, # buf1); lpt1[buffered(m0).leb] := mklp (lpt1[buffered(m0).leb].ref-size, lpt1[buffered(m0).leb].size + # buf1, lpt1[buffered(m0).leb].flags, lpt1[buffered(m0).leb].gcheapidx)} else lpt1[buffered(m0).leb] := mklp(lpt1[buffered(m0).leb].ref-size, LEB_SIZE, lpt1[buffered(m0).leb].flags, lpt1[buffered(m0).leb].gcheapidx)] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(buffered(m0), log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, buffered(m0), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, buffered(m0)) ∧ # lpt0 = # avol → ⟨pstate := index(m0); apersistence_add_ind#(ind, adr0, istore0, ginval, gstore, gstore0, log1, m, ns0; adr2, istore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ readonly → m0 = pstate.lnum) ∧ adr = adr2 ∧ err = err0))

User applied rule insert program lemma

And obtained the following new goals

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(m0), ns0, lpt0, log1, m, adr0, buf1, # buf1, isbuf2, 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)% ⊦ ¬ natkey < natkey; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic