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Proof step 130 from proof refine-allocate-ind (previous step)

# lpt0 = # avol0, # lpt2 = # avol0, lpt2[n0] = mklp(0, m5, LP_FREE, m6), keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n0 < # avol0, ginval < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), istore0 ⊑ istore, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb = nobuffer ⊦ bleb = buffered(n0), pstate = readonly, dups(log1), ( bleb ≠ nobuffer → avol0[n0, mapped(mkbuf(0))][bleb.leb].mapped? ∧ bleb.leb < # avol0[n0, mapped(mkbuf(0))] ∧ n0 < # avol0 ∧ bleb.isbuf?) ∧ ( bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE) → (n0 < # avol0[n0, mapped(mkbuf(0))] ∧ n0 < # avol0) ∧ ( avol0[n0, mapped(mkbuf(0))][n0].mapped? → avol0[n0, mapped(mkbuf(0))][n0].mapped? ∧ n0 < # avol0[n0, mapped(mkbuf(0))] ∧ n0 < # avol0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 131:
# lpt2 = # avol0, # lpt0 = # avol0, avol0[pstate.lnum] = unmapped, lpt2[n0] = mklp(0, m5, LP_FREE, m6), keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate.lnum < # avol0, ginval < # avol0, n0 < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, buffered(pstate.lnum)), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt2, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), istore0 ⊑ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore ⊦ pstate.lnum = n0, pstate = unbuffered, pstate = readonly, dups(log1)

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ aleb.mapped? ↔ aleb ≠ unmapped; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ buffered(m).isbuf?; (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ nobuffer ≠ buffered(m); (s)%m ≠ n ⊦ avol[m, aleb][n] = avol[n]; (s)% ⊦ buffered(m).leb = m; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ # avol[n, aleb] = # avol; (s)