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Proof step 193 from proof refine-add-gnds (previous step)

# gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n1 = dom gstore ∪ ginval, gstore[n1] = groupblock(gndx1, lax1, m1), avol[n1] = mapped(buf1), lpt1[n1] = mklp(m1, # buf1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, nx + n1 '), pstate = journal(n1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval ∩ elems nx = ∅, gndx0 ≠ [], n ≠ 0, n1 < # avol, ginval < # avol, n < gndx0.flashsize, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol, buffered(n1)), awbuf-inv(avol[n1, mapped(buf1 + subarray(buf0, 0, n))], buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol), bufs-log-only(buffered(n1), nx + n1 ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), inv(groupblock(gndx1, lax1, m1)), is-aligned(# buf1 + n, EB_PAGE_SIZE), log-group-block(nx + n1 ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n1 '), n1 ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , ¬ dups(nx), ¬ n1 ∈ ginval, ¬ n1 ∈ nx, isbuf1 → synced(avol) ⊦ pstate.lnum ∈ gstore ∧ (pstate.index? ∨ pstate.journal?) ∧ (∃ lax, err. (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(lax1 + lax) ∧ # lax ≤ # lax0 ∧ inv-flashsize(prefixn(# lax, gndx0), lax) ∧ (err = ESUCCESS ↔ # lax = # lax0) ∧ ⟨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[n1, mapped(avol[n1].data + subarray(buf0, 0, n))], lpt1[n1, mklp(lpt1[n1].ref-size, LEB_SIZE, lpt1[n1].flags, lpt1[n1].gcheapidx)], gstore, ginval) ∧ pstate = readonly ∧ lax0.to-adr(n1) = ax ∧ err1 = err0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 194:
# lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, (elems nx ∪ dom gstore0) ++ n1 = dom gstore ∪ ginval, lpt1[n1] = mklp(m1, # buf1, LP_GROUP_NODES, m2), avol[n1] = mapped(buf1), gstore[n1] = groupblock(gndx1, lax1, m1), lpt1[n1] = mklp(m, m0, lpf, m3), keyset(gch) = gc-heap(lpt1, nx + n1 '), pstate = journal(n1), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, n < gndx0.flashsize, ginval < # avol, n1 < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol[n1, mapped(buf1 + subarray(buf0, 0, n))], buffered(n1)), awbuf-inv(avol, buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol), bufs-log-only(buffered(n1), nx + n1 ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx1, lax1, m1)), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval), is-aligned(# buf1 + n, EB_PAGE_SIZE), log-group-block(nx + n1 ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n1 '), n1 ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , isbuf1 → synced(avol) ⊦ pstate.lnum ∈ gstore ∧ (pstate.index? ∨ pstate.journal?) ∧ (∃ lax, err. (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(lax1 + lax) ∧ # lax ≤ # lax0 ∧ inv-flashsize(prefixn(# lax, gndx0), lax) ∧ (err = ESUCCESS ↔ # lax = # lax0) ∧ ⟨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[n1, mapped(avol[n1].data + subarray(buf0, 0, n))], lpt1[n1, mklp(m, LEB_SIZE, lpf, m3)], gstore, ginval) ∧ pstate = readonly ∧ lax0.to-adr(n1) = ax ∧ err1 = err0)), gndx0 = [], n = 0, dups(nx), n1 ∈ ginval, n1 ∈ nx

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt1[n1], m, m0, lpf, m3]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt1[n1], m, m0, lpf, m3