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Proof step 50 from proof inv-allocate-ind (previous step)

# lpt0 = # avol0, # lpt = # avol0, # lpt0 = # avol0[n0, mapped(mkbuf(0))], isbuf0 ↔ false, lpt[n0] = mklp(0, m1, LP_FREE, m2), adr0 = adr, avol1 = avol0[n0, mapped(mkbuf(0))], keyset(gch) = gc-heap(lpt, log0), lpt2 = lpt0, m3 = n0, m4 = 0, m5 = m, ns0 = ns, nx1 = log0, n0 < # avol0, awbuf-inv(avol0, bleb), awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log0, lpt), freelist-cons(lpt, n0 ' + nx0), log-group-block(log0, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log0), synced(avol0), bleb = buffered(n0) ∨ (bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE)) ∧ n0 < # avol0[n0, mapped(mkbuf(0))] ∧ avol0[n0, mapped(mkbuf(0))][n0].mapped? ∧ 0 = # avol0[n0, mapped(mkbuf(0))][n0].data ⊦ [awbuf_move_buf#(n0, 0, adr, m, log0, avol0[n0, mapped(mkbuf(0))], lpt0, ns, false; bleb; err)] ( awbuf-inv(avol1, bleb) → ⟪lpt1 := lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)] [n0, lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)][n0].ref-size:= 0 ]; freelist := (n0 ' + nx0).tail; if err ≠ ESUCCESS then freelist := n0 ' + freelist else lpt1[n0].flags := LP_INDEX_NODES⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb, log0, lpt1) ∧ # lpt1 = # avol0 ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(false, bleb, lpt1, avol0[n0, mapped(mkbuf(0))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb))), buffered(n0) = bleb

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
# lpt = # avol0, # lpt0 = # avol0, lpt[n0] = mklp(0, m1, LP_FREE, m2), keyset(gch) = gc-heap(lpt, log0), buffered(n0) ≠ bleb, n0 < # avol0, awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log0, lpt), freelist-cons(lpt, n0 ' + nx0), log-group-block(log0, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log0), synced(avol0), bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE) ⊦ [awbuf_move_buf#(n0, 0, adr, m, log0, avol0[n0, mapped(mkbuf(0))], lpt0, ns, false; bleb; err)] ( awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb) → ⟪lpt1 := lpt[n0, lpt[n0, mklp(lpt[n0].ref-size, 0, lpt[n0].flags, lpt[n0].gcheapidx)][n0].ref-size:= 0]; freelist := (n0 ' + nx0).tail; if err ≠ ESUCCESS then freelist := n0 ' + freelist else lpt1[n0].flags := LP_INDEX_NODES⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb, log0, lpt1) ∧ # lpt1 = # avol0 ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(false, bleb, lpt1, avol0[n0, mapped(mkbuf(0))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0)))

Rule argument

Additional information

Used simplifier rules: m < # lpt ⊦ lpt[m, lp][m, lp0] = lpt[m, lp0]; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ # mkbuf(n) = n; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ # avol[n, aleb] = # avol; (s)