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Proof step 105 from proof refine-add-gnds (previous step)

# gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, gstore[n] = groupblock(gndx1, lax1, m0), avol[n] = mapped(buf), lpt1[n] = mklp(m0, m1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, nx + n '), pstate = journal(n), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval ∩ elems nx = ∅, LEB_SIZE < m1 + gndx0.flashsize, n < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, m1, gndx0, lax0, false), 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(groupblock(gndx1, lax1, m0)), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), 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, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ (⌊ENOSPC⌋ ∨ ENOSPC = ESUCCESS) ∧ ¬ dups(lax1 + []) ∧ # [] ≤ # lax0 ∧ inv-flashsize(prefixn(# [], gndx0), []) ∧ (ENOSPC = ESUCCESS ↔ # [] = # lax0) ∧ ⟨ax := ([]).to-adr(pstate.lnum), err0 := ENOSPC; gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist + prefixn(# [], gndx0); 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 = readonly ∧ lax0.to-adr(n) = ax ∧ ENOSPC = err0), gndx0 = [], dups(nx), n ∈ ginval, n ∈ nx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 106:
# gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, gstore[n] = groupblock(gndx1, lax1, m0), avol[n] = mapped(buf), lpt1[n] = mklp(m0, m1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, nx + n '), pstate = journal(n), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval ∩ elems nx = ∅, gndx0 ≠ [], lax0 ≠ [], LEB_SIZE < m1 + gndx0.flashsize, n < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, m1, gndx0, lax0, false), 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(groupblock(gndx1, lax1, m0)), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), 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, istore1 ⊑ istore2, ¬ dups(nx), ¬ n ∈ ginval, ¬ n ∈ nx, isbuf1 → synced(avol) ⊦ ⟨ax := ([]).to-adr(pstate.lnum), err0 := ENOSPC; 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 = readonly ∧ lax0.to-adr(n) = ax ∧ ENOSPC = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ # gndx = 0 ↔ gndx = []; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gndx + [] = gndx; (s)% ⊦ # lax = 0 ↔ lax = []; (s)% ⊦ ESUCCESS ≠ ENOSPC; (s)% ⊦ inv-flashsize([], lax) ↔ lax = []; (s)% ⊦ prefixn(0, gndx) = []; (s)% ⊦ 0 ≤ m; (s)% ⊦ # [] = 0; (s)% ⊦ inv(groupblock(gndx, lax, m0)) → ¬ dups(lax); (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ lax + [] = lax; (s)% ⊦ ⌊ENOSPC⌋ ; (s)