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Proof step 133 from proof refine-add-gnds (previous step)

# lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, isbuf ↔ isbuf1, gstore[n] = groupblock(gndx1, lax, m1), lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), avol[n] = mapped(buf1), adr = adr0, ax = ax0, gndx = gndx0, istore = istore1, istore0 = istore2, keyset(gch) = gc-heap(lpt1, nx + n '), log = nx + n ', maxino = m0, ns = ns0, pstate = journal(n), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, n < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol, buffered(n)), awbuf-inv(avol[n, mapped(buf1 + buf0)], buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx1, lax, m1)), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ ⟨if pstate.journal? ∨ pstate = readonly then if pstate = readonly then err0 := EROFS else {choose lax, err with (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(gstore[pstate.lnum].ladrlist + lax) ∧ # lax ≤ # gndx ∧ inv-flashsize(prefixn(# lax, gndx), lax) ∧ (err = ESUCCESS ↔ # lax = # gndx) in {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 := ?} else abort⟩ ( abs-gstore (avol[pstate.lnum, mapped(avol[pstate.lnum].data + buf0)], lpt1 [pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, lpt1[pstate.lnum].size + gndx0.flashsize, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx) ], gstore, ginval) ∧ (isbuf → is-aligned(# avol[pstate.lnum].data + # buf0, EB_PAGE_SIZE)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ n = pstate.lnum ∧ lax0.to-adr(pstate.lnum) = ax ∧ ESUCCESS = err0), gndx0 = [], dups(nx), n ∈ ginval, n ∈ nx

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 134:
# gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, isbuf ↔ isbuf1, avol[n] = mapped(buf1), lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx1, lax, m1), adr = adr0, ax = ax0, gndx = gndx0, istore = istore1, istore0 = istore2, keyset(gch) = gc-heap(lpt1, nx + n '), log = nx + n ', maxino = m0, ns = ns0, pstate = journal(n), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval ∩ elems nx = ∅, ginval < # avol, n < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol[n, mapped(buf1 + buf0)], buffered(n)), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), inv(groupblock(gndx1, lax, m1)), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ ⟨if pstate = readonly then err0 := EROFS else {choose lax, err with (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(gstore[pstate.lnum].ladrlist + lax) ∧ # lax ≤ # gndx ∧ inv-flashsize(prefixn(# lax, gndx), lax) ∧ (err = ESUCCESS ↔ # lax = # gndx) in {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[pstate.lnum, mapped(avol[pstate.lnum].data + buf0)], lpt1 [pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, lpt1[pstate.lnum].size + gndx0.flashsize, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx) ], gstore, ginval) ∧ (isbuf → is-aligned(# avol[pstate.lnum].data + # buf0, EB_PAGE_SIZE)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ n = pstate.lnum ∧ lax0.to-adr(pstate.lnum) = ax ∧ ESUCCESS = err0), gndx0 = [], dups(nx), n ∈ nx, n ∈ ginval

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ journal(m).journal?; (s)