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Proof step 52 from proof refine-add-gnds (previous step)

# lpt1 = # avol, # lpt0 = # avol, isbuf ↔ isbuf1, gstore[log1.last] = groupblock(gndx0, lax0, m0), lpt1[log1.last] = mklp(m0, m1, LP_GROUP_NODES, m2), avol[log1.last] = mapped(buf), adr = adr0, ax = ax0, gndx = [], istore = istore1, istore0 = istore2, keyset(gch) = gc-heap(lpt1, log1), log = log1, maxino = m, ns = ns0, pstate = journal(log1.last), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, log1.last < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(log1.last), lpt1, avol), bufs-log-only(buffered(log1.last), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval), inv(groupblock(gndx0, lax0, m0)), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), log1.last ∈ gstore, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ ∃ lax, err. (⌊err⌋ ∨ err = ESUCCESS → pstate.lnum ∈ gstore ∧ (pstate.index? ∨ pstate.journal?)) ∧ ( (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(gstore[pstate.lnum].ladrlist + lax) ∧ # lax ≤ # gndx ∧ inv-flashsize(prefixn(# lax, gndx), lax) ∧ (err = ESUCCESS ↔ # lax = # gndx)) ∧ ⟨ax := lax.to-adr(pstate.lnum), err0 := err; gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist + prefixn(# lax, gndx); gstore[pstate.lnum].ladrlist := gstore[pstate.lnum].ladrlist + lax; if err0 ≠ ESUCCESS then ax := ?, pstate := readonly; isbuf := ?⟩ ( abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf → synced(avol)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ log1.last = pstate.lnum ∧ [] = ax ∧ ESUCCESS = err0), log1 = [], dups(log1), log1.last ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
# lpt0 = # avol, # lpt1 = # avol, avol[log1.last] = mapped(buf), lpt1[log1.last] = mklp(m0, m1, LP_GROUP_NODES, m2), gstore[log1.last] = groupblock(gndx0, lax0, m0), keyset(gch) = gc-heap(lpt1, log1), pstate = journal(log1.last), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, log1 ≠ [], ginval < # avol, log1.last < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(log1.last), lpt1, avol), bufs-log-only(buffered(log1.last), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), inv(groupblock(gndx0, lax0, m0)), 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), log1.last ∈ gstore, istore1 ⊑ istore2, ¬ dups(log1), ¬ log1.last ∈ ginval, isbuf1 → synced(avol) ⊦ pstate.lnum ∈ gstore ∧ (pstate.index? ∨ pstate.journal?) ∧ ¬ dups(gstore[pstate.lnum].ladrlist) ∧ ⟨ax := [], err0 := ESUCCESS; gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist; gstore[pstate.lnum].ladrlist := gstore[pstate.lnum].ladrlist; if err0 ≠ ESUCCESS then ax := ?, pstate := readonly; isbuf1 := ?⟩ ( abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ log1.last = pstate.lnum ∧ [] = ax ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: fwd-inv-gblock-rem: ⊦ inv(gstore \ ginval) ∧ n ∈ gstore ∧ ¬ n ∈ ginval ∧ gstore[n] = gblock → inv(gblock); (forward) from specification apersistence-base% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ lax + [] = lax; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gndx + [] = gndx; (s)% ⊦ ([]).to-adr(n) = []; (s)% ⊦ inv-flashsize([], lax) ↔ lax = []; (s)% ⊦ prefixn(0, gndx) = []; (s)% ⊦ # [] = 0; (s)% ⊦ # lax = 0 ↔ lax = []; (s)% ⊦ m ≤ 0 ↔ m = 0; (s)% ⊦ # [] = 0; (s)