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Proof step 7 from proof inv-add-ind (previous step)

# lpt = # avol, # lpt0 = # avol, isbuf0 ↔ isbuf1, lpt[bleb.leb] = mklp(m, m3, lpf, m2), adr = adr1, adr0 = adr2, bleb0 = bleb, keyset(gch) = gc-heap(lpt, log0), log = log0, m1 = LEB_SIZE, awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf1, bleb, lpt, avol), bufs-log-only(bleb, log0, lpt), freelist-cons(lpt, freelist), log-group-block(log0, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log0), ¬ isbuf1 → bleb.isbuf? ∧ bleb.leb < # avol ∧ lpf = LP_INDEX_NODES ∧ avol[bleb.leb].mapped? ∧ (m3 + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → m3 = # avol[bleb.leb].data) ⊦ ⟪awbuf_is_readonly#(adr0, m0, log, avol, lpt0, ns, bleb0, isbuf0; ; isbuf); if isbuf then err := EROFS else let buf = mkbuf(ind.flashsize), m = ?, bleb = ? in {awbuf_get_buf#(adr0, m0, log, avol, lpt0, ns, bleb0, isbuf0; ; bleb); encode_index_node#(ind, 0; m, buf; err); if err = ESUCCESS then if ¬ lpt[bleb.leb].size + m ≤ m1 then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m0, log, avol, lpt0, ns, bleb0; ; isbuf0); err := ENOSPC} else {awbuf_write_buf#(m, buf, adr0, m0, log, lpt0, ns, bleb0; avol, isbuf0; err); if err = ESUCCESS then {adr := @(bleb.leb, lpt[bleb.leb].size, m); lpt[bleb.leb].size := lpt[bleb.leb].size + m} else lpt[bleb.leb].size := m1} else {debug#("persistence: could not encode index node"); awbuf_enter_readonly#(adr0, m0, log, avol, lpt0, ns, bleb0; ; isbuf0)}}⟫ ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log0) ∧ bufs-log-only(bleb, log0, lpt) ∧ # lpt = # avol ∧ log-group-block(log0, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log0) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# lpt0 = # avol, # lpt = # avol, lpt[bleb.leb] = mklp(m, m3, lpf, m2), keyset(gch) = gc-heap(lpt, log0), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf1, bleb, lpt, avol), bufs-log-only(bleb, log0, lpt), freelist-cons(lpt, freelist), log-group-block(log0, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log0), ¬ isbuf1 → bleb.isbuf? ∧ bleb.leb < # avol ∧ lpf = LP_INDEX_NODES ∧ avol[bleb.leb].mapped? ∧ (m3 + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → m3 = # avol[bleb.leb].data) ⊦ ⟪awbuf_is_readonly#(adr0, m0, log0, avol, lpt0, ns, bleb, isbuf1; ; isbuf); if isbuf then err := EROFS else let buf = mkbuf(2 * NODE_HEADER_SIZE + ind.alignedsize), m = ?, bleb1 = ? in {awbuf_get_buf#(adr0, m0, log0, avol, lpt0, ns, bleb, isbuf1; ; bleb1); encode_index_node#(ind, 0; m, buf; err); if err = ESUCCESS then if ¬ lpt[bleb1.leb].size + m ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m0, log0, avol, lpt0, ns, bleb; ; isbuf1); err := ENOSPC} else {awbuf_write_buf#(m, buf, adr0, m0, log0, lpt0, ns, bleb; avol, isbuf1; err); if err = ESUCCESS then {adr := @(bleb1.leb, lpt[bleb1.leb].size, m); lpt[bleb1.leb] := mklp(lpt[bleb1.leb].ref-size, lpt[bleb1.leb].size + m, lpt[bleb1.leb].flags, lpt[bleb1.leb].gcheapidx)} else lpt[bleb1.leb] := mklp(lpt[bleb1.leb].ref-size, LEB_SIZE, lpt[bleb1.leb].flags, lpt[bleb1.leb].gcheapidx)} else {debug#("persistence: could not encode index node"); awbuf_enter_readonly#(adr0, m0, log0, avol, lpt0, ns, bleb; ; isbuf1)}}⟫ ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log0) ∧ bufs-log-only(bleb, log0, lpt) ∧ # lpt = # avol ∧ log-group-block(log0, lpt) ∧ buf-ro-rw-mode(isbuf1, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log0) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol)

Rule argument

Additional information

Used simplifier rules: elim-lp-upd-size: ⊦ lp.size:= n = mklp(lp.ref-size, n, lp.flags, lp.gcheapidx);% ⊦ ind.flashsize = 2 * NODE_HEADER_SIZE + ind.alignedsize; (s)