[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 25 from proof refine-read-gnd (previous step)

# gndx = # lax1 + # lax0 + 1, # lpt0 = # avol, # lpt = # avol, gstore[m0] = groupblock(gndx, lax1 + @(m1, m2) ' + lax0, m3), lpt[m0] = mklp(m3, m4, LP_GROUP_NODES, m5), avol[m0] = mapped(buf), gnd = gnd0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, m0 < # avol, ginval < # avol, abs-istore(avol, lpt, istore), abs-nodes(buf, gndx, lax1 + @(m1, m2) ' + lax0, m4 = LEB_SIZE), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(groupblock(gndx, lax1 + @(m1, m2) ' + lax0, m3)), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), m0 ∈ gstore, istore0 ⊑ istore, m4 ≠ LEB_SIZE → m4 = # buf, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol), abs-nodes(buf, gndx, lax1 + @(m1, m2) ' + lax0, m4 = LEB_SIZE) → (∃ buf0, buf1, buf2, gndx0, gnd, gndx1. gndx = gndx0 + gnd ' + gndx1 ∧ # gndx0 = # lax1 ∧ buf = buf0 + buf1 + buf2 ∧ @(m1, m2) = @(# buf0, gnd.flashsize) ∧ # buf1 = gnd.flashsize ∧ abs-node(buf1, gnd)) ⊦ ⟪persistence_read_gnd#(@(m0, m1, m2), adr1, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; gnd; err)⟫ ⟨apersistence_read_gnd#(@(m0, m1, m2), adr1, istore, istore0, ginval, gstore, gstore0, log1, m, ns0, pstate, isbuf; gnd0; err0)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ gnd = gnd0 ∧ err = err0), dups(log1), m0 ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
# gndx1 = # lax0, # lpt0 = # avol, # lpt = # avol, # buf1 = 2 * NODE_HEADER_SIZE + gnd1.alignedsize, # gndx0 = # lax1, gstore[m0] = groupblock(gndx0 + gnd1 ' + gndx1, lax1 + @(# buf0, # buf1) ' + lax0, m3), lpt[m0] = mklp(m3, m4, LP_GROUP_NODES, m5), avol[m0] = mapped(buf0 + buf1 + buf2), gnd = gnd0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, m0 < # avol, ginval < # avol, abs-istore(avol, lpt, istore), abs-node(buf1, gnd1), abs-nodes(buf0 + buf1 + buf2, gndx0 + gnd1 ' + gndx1, lax1 + @(# buf0, # buf1) ' + lax0, m4 = LEB_SIZE), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(groupblock(gndx0 + gnd1 ' + gndx1, lax1 + @(# buf0, # buf1) ' + lax0, m3)), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), m0 ∈ gstore, istore0 ⊑ istore, ¬ dups(log1), ¬ m0 ∈ ginval, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol), m4 ≠ LEB_SIZE → m4 = # buf0 + # buf1 + # buf2 ⊦ ⟪persistence_read_gnd#(@(m0, # buf0, # buf1), adr1, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; gnd; err)⟫ ⟨apersistence_read_gnd# (@(m0, # buf0, # buf1), adr1, istore, istore0, ginval, gstore, gstore0, log1, m, ns0, pstate, isbuf; gnd0; err0)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ gnd = gnd0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ #(ladr ' + lax) = (# lax)+1; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)%abs-nodes-elems-adr-length: ⊦ abs-nodes(buf, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]%fwd-inv-gblock-rem: ⊦ inv(gstore \ ginval) ∧ n ∈ gstore ∧ ¬ n ∈ ginval ∧ gstore[n] = gblock → inv(gblock); (forward) from specification apersistence-base%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ m +1 = m + 1; (s)% ⊦ #(gnd ' + gndx) = (# gndx)+1; (s)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)% ⊦ @(m, m0) = @(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ gnd.flashsize = 2 * NODE_HEADER_SIZE + gnd.alignedsize; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]