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Proof step 62 from proof inv-allocate-ind (previous step)

# lpt0 = # avol0, # lpt2 = # avol0, lpt2[n0] = mklp(0, m3, LP_FREE, m2), err = ESUCCESS, err = err0, freelist = (n0 ' + nx0).tail, keyset(gch) = gc-heap(lpt2, log0), lpt1 = lpt2[n0, lpt2[n0, mklp(lpt2[n0].ref-size, 0, lpt2[n0].flags, lpt2[n0].gcheapidx)][n0].ref-size:= 0], n0 < # avol0, n0 < # lpt2[n0, mklp(lpt2[n0].ref-size, 0, lpt2[n0].flags, lpt2[n0].gcheapidx)], n0 < # lpt2, awbuf-inv(avol0, bleb), awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), awbuf-inv(avol0[n0, mapped(mkbuf(0))], buffered(n0)), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log0, lpt2), freelist-cons(lpt2, n0 ' + nx0), log-group-block(log0, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log0), synced(avol0), bleb ≠ nobuffer → avol0[n0, mapped(mkbuf(0))][bleb.leb].mapped? ∧ bleb.leb < # avol0 ∧ bleb.isbuf?, ⌊err0⌋ ∨ err0 = ESUCCESS, bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE) ⊦ ⟪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(buffered(n0), log0, lpt1) ∧ # lpt1 = # avol0 ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(false, buffered(n0), lpt1, avol0[n0, mapped(mkbuf(0))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0)), n0 ' + nx0 = [], buffered(n0) = bleb

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 63:
# lpt2 = # avol0, # lpt0 = # avol0, lpt2[n0] = mklp(0, m3, LP_FREE, m2), err = err0, err = ESUCCESS, freelist = (n0 ' + nx0).tail, keyset(gch) = gc-heap(lpt2, log0), lpt1 = lpt2[n0, lpt2[n0, mklp(lpt2[n0].ref-size, 0, lpt2[n0].flags, lpt2[n0].gcheapidx)][n0].ref-size:= 0], n0 < # lpt1, n0 < # lpt2, n0 < # lpt2[n0, mklp(lpt2[n0].ref-size, 0, lpt2[n0].flags, lpt2[n0].gcheapidx)], n0 < # avol0, awbuf-inv(avol0[n0, mapped(mkbuf(0))], buffered(n0)), awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log0, lpt2), freelist-cons(lpt2, n0 ' + nx0), log-group-block(log0, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log0), synced(avol0), bleb ≠ nobuffer → avol0[n0, mapped(mkbuf(0))][bleb.leb].mapped? ∧ bleb.leb < # avol0 ∧ bleb.isbuf?, bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ n0 ' + nx0 = [], buffered(n0) = bleb, lpt-free-unref(lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES]) ∧ freelist-cons(lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES], freelist) ∧ bin-heap-inv(gch, lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES]) ∧ keyset(gch) = gc-heap(lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES], log0) ∧ bufs-log-only(buffered(n0), log0, lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES]) ∧ # lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES] = # avol0 ∧ log-group-block(log0, lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES]) ∧ buf-ro-rw-mode(false, buffered(n0), lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES], avol0[n0, mapped(mkbuf(0))]) ∧ lpt-leb-size(lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES]) ∧ lpt-ram-flash(lpt1[n0, lpt1[n0].flags:= LP_INDEX_NODES], lpt0, log0)

Rule argument

Additional information

Used simplifier rules: ⊦ n ' + nx ≠ []; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ # lpt[n, lp] = # lpt; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)% ⊦ mklp(m, m0, lpf, m1).ref-size:= m2 = mklp(m2, m0, lpf, m1); (s)