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Proof step 45 from proof inv-allocate-ind (previous step)

# lpt0 = # avol, # lpt0 = # avol0, # lpt = # avol0, isbuf1 ↔ false, lpt[n0] = mklp(0, m1, LP_FREE, m2), avol = avol0[n0, mapped(mkbuf(0))], err = err0, err = ESUCCESS, freelist = freelist0.tail, freelist0 = n0 ' + nx0, keyset(gch) = gc-heap(lpt, log0), lpt1 = lpt[n, mklp(lpt[n].ref-size, 0, lpt[n].flags, lpt[n].gcheapidx)] [n, lpt[n, mklp(lpt[n].ref-size, 0, lpt[n].flags, lpt[n].gcheapidx)][n].ref-size:= 0 ], n = n0, n0 < # avol0, n < # lpt[n, mklp(lpt[n].ref-size, 0, lpt[n].flags, lpt[n].gcheapidx)], n < # lpt, awbuf-inv(avol, 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(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log0), synced(avol0), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪awbuf_move_buf#(n, 0, adr, m, log0, avol, lpt0, ns, isbuf1; bleb; err); if err ≠ ESUCCESS then freelist := n ' + freelist else lpt1[n].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 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb)), buffered(n0) = bleb, freelist0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
# 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, 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(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log0), synced(avol0) ⊦ ⟪awbuf_move_buf#(n0, 0, adr, m, log0, avol0[n0, mapped(mkbuf(0))], lpt0, ns, false; bleb; err); 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))

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ m < n → n ≠ 0; (s)%freelist-cons-first-free: ⊦ freelist-cons(lpt, n ' + freelist) → n < # lpt ∧ lpt[n].flags = LP_FREE; (forward) from specification persistence-base%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ # lpt[n, lp] = # lpt; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ n ' + nx ≠ []; (s)% ⊦ # avol[n, aleb] = # avol; (s)