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Proof step 311 from proof refine-add-gnds (previous step)

# lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, avol[n] = mapped(buf), lpt1[n] = mklp(m0, m1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx1, lax0, m0), keyset(gch) = gc-heap(lpt1, nx + n '), pstate = journal(n), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval ∩ elems nx = ∅, gndx0 ≠ [], n < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), 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, lax0, m0)), 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, ⌊err1⌋ , ¬ dups(nx), ¬ n ∈ nx, ¬ n ∈ ginval, m1 + gndx0.flashsize ≤ LEB_SIZE → m1 = # buf, isbuf1 → synced(avol) ⊦ pstate.lnum ∈ gstore ∧ (pstate.index? ∨ pstate.journal?) ∧ (∃ lax, err. (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(gstore[pstate.lnum].ladrlist + lax) ∧ # lax ≤ # gndx0 ∧ inv-flashsize(prefixn(# lax, gndx0), lax) ∧ (err = ESUCCESS ↔ # lax = # gndx0) ∧ ⟨ax := lax.to-adr(pstate.lnum), err0 := err; gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist + prefixn(# lax, gndx0); gstore[pstate.lnum].ladrlist := gstore[pstate.lnum].ladrlist + lax; if err0 ≠ ESUCCESS then ax := ?, pstate := readonly; isbuf1 := ?⟩ (abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf1 → synced(avol)) ∧ pstate = readonly ∧ ax1 = ax ∧ err1 = err0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 312:
# lpt1 = # avol, # lpt0 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, gstore[n] = groupblock(gndx1, lax0, m0), lpt1[n] = mklp(m0, m1, LP_GROUP_NODES, m2), avol[n] = mapped(buf), gstore[pstate.lnum] = groupblock(gndx, lax1, m), keyset(gch) = gc-heap(lpt1, nx + n '), pstate = journal(n), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, ginval < # avol, n < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), 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, lax0, m0)), 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, istore1 ⊑ istore2, ⌊err1⌋ , isbuf1 → synced(avol), m1 + gndx0.flashsize ≤ LEB_SIZE → m1 = # buf ⊦ pstate.lnum ∈ gstore ∧ (pstate.index? ∨ pstate.journal?) ∧ (∃ lax, err. (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(lax1 + lax) ∧ # lax ≤ # gndx0 ∧ inv-flashsize(prefixn(# lax, gndx0), lax) ∧ (err = ESUCCESS ↔ # lax = # gndx0) ∧ ⟨ax := lax.to-adr(pstate.lnum), err0 := err; gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist + prefixn(# lax, gndx0); gstore[pstate.lnum].ladrlist := gstore[pstate.lnum].ladrlist + lax; if err0 ≠ ESUCCESS then ax := ?, pstate := readonly; isbuf1 := ?⟩ (abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf1 → synced(avol)) ∧ pstate = readonly ∧ ax1 = ax ∧ err1 = err0)), gndx0 = [], dups(nx), n ∈ nx, n ∈ ginval

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore[pstate.lnum], gndx, lax1, m]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore[pstate.lnum], gndx, lax1, m