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Proof step 357 from proof refine-sync (previous step)

# lpt1 = # avol, # lpt0 = # avol, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m, # buf0, lpf, m4), avol[pstate.lnum] = mapped(buf0), gc-heap(lpt1, log1) = gc-heap(lpt1[pstate.lnum, mklp(m, LEB_SIZE, lpf, m4)], log1), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, pstate.lnum < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore2, ginval), abs-istore(avol, lpt1, istore2), abs-padding(buf1), awbuf-inv(avol, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore1), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), log-group-block(log1, lpt1[pstate.lnum, mklp(m, LEB_SIZE, lpf, m4)]), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m, LEB_SIZE, lpf, m4)], lpt0, log1), # buf0 + # buf1 ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), lpf = LP_FREE, pstate = readonly, pstate = unbuffered, dups(log1), is-aligned(# buf0, EB_PAGE_SIZE), abs-istore(avol, lpt1[pstate.lnum, mklp(m, LEB_SIZE, lpf, m4)], istore2) ∧ abs-gstore(avol, lpt1[pstate.lnum, mklp(m, LEB_SIZE, lpf, m4)], gstore2, ginval)

User applied rule constructor cut

And closed the goal!

Rule argument

var: lpf

Additional information

Used simplifier rules: lpropflags, lprops freely generated by LP_FREE, LP_GROUP_NODES, LP_INDEX_NODES, mklp ;;% ⊦ LP_GROUP_NODES ≠ LP_INDEX_NODES; (s)%lpf0 ≠ LP_GROUP_NODES, lpf1 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → gc-heap(lpt[n, mklp(n0, n1, lpf1, n2)], nx) = gc-heap(lpt, nx); (s)% ⊦ LP_FREE ≠ LP_INDEX_NODES; (s)%n < # lpt, lpf ≠ LP_GROUP_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) ∧ log-group-block(nx, lpt) → log-group-block(nx, lpt[n, lp]); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # avol ⊦ lpt[n] = mklp(n0, n1, LP_INDEX_NODES, n2) ∧ abs-istore(avol, lpt, istore) → abs-istore (avol, lpt[n, mklp(n0, LEB_SIZE, LP_INDEX_NODES, n2)], istore); (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)%lpf ≠ LP_GROUP_NODES, lp.flags ≠ LP_GROUP_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) → ( abs-gstore(avol, lpt[n, lp], gstore, ginval) ↔ abs-gstore(avol, lpt, gstore, ginval)); (s)%n < # lpt ⊦ lpt[n] = mklp(m0, m1, LP_GROUP_NODES, m2) → gc-heap(lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)], nx) = gc-heap(lpt, nx); (s)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)%n < # lpt ⊦ lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ log-group-block(nx, lpt) → log-group-block(nx, lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)]); (s)%lpf ≠ LP_INDEX_NODES, lp.flags ≠ LP_INDEX_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) → ( abs-istore(avol, lpt[n, lp], istore) ↔ abs-istore(avol, lpt, istore)); (s)%n < # avol ⊦ lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ abs-gstore(avol, lpt, gstore, ginval) → abs-gstore (avol, lpt[n, mklp(n0, LEB_SIZE, LP_GROUP_NODES, n2)], gstore, ginval); (s)