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Proof step 17 from proof inv-add-ind (previous step)

# lpt0 = # avol, # lpt1 = # avol, isbuf ↔ false, avol[n] = mapped(buf0), lpt1[n] = mklp(m1, m3, LP_INDEX_NODES, m2), adr = adr0, bleb0 = buffered(n), buf = mkbuf(2 * NODE_HEADER_SIZE + ind.alignedsize), keyset(gch) = gc-heap(lpt1, log0), log = log0, lpt = lpt0, m = m0, n < # avol, awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), log-group-block(log0, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log0), m3 + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → m3 = # buf0 ⊦ ⟪encode_index_node#(ind, 0; m, buf; err); isbuf1 := false; bleb1 := buffered(n); if err = ESUCCESS then if ¬ lpt1[bleb0.leb].size + m ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m0, log0, avol, lpt0, ns, bleb1; ; isbuf1); err := ENOSPC} else {awbuf_write_buf#(m, buf, adr0, m0, log0, lpt0, ns, bleb1; avol, isbuf1; err); if err = ESUCCESS then {adr := @(bleb0.leb, lpt1[bleb0.leb].size, m); lpt1[bleb0.leb] := mklp(lpt1[bleb0.leb].ref-size, lpt1[bleb0.leb].size + m, lpt1[bleb0.leb].flags, lpt1[bleb0.leb].gcheapidx)} else lpt1[bleb0.leb] := mklp(lpt1[bleb0.leb].ref-size, LEB_SIZE, lpt1[bleb0.leb].flags, lpt1[bleb0.leb].gcheapidx)} else {debug#("persistence: could not encode index node"); awbuf_enter_readonly#(adr0, m0, log0, avol, lpt0, ns, bleb1; ; isbuf1)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb1, log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol)

User applied rule insert program lemma

And obtained the following new goals

Proof step 18:
n + ind.flashsize ≤ # buf, buf0 = buf ⊦ ⟪encode_index_node#(ind, n; m, buf; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ subarray(buf, 0, n) = subarray(buf0, 0, n) ∧ subarray(buf, n + ind.flashsize, # buf0 - n + ind.flashsize) = subarray(buf0, n + ind.flashsize, # buf0 - n + ind.flashsize) ∧ (err = ESUCCESS → abs-node(subarray(buf, n, ind.flashsize), ind) ∧ m = ind.flashsize))
Proof step 19:
# lpt1 = # avol, # lpt0 = # avol, isbuf ↔ false, lpt1[n] = mklp(m1, m3, LP_INDEX_NODES, m2), avol[n] = mapped(buf0), adr = adr0, bleb0 = buffered(n), buf = mkbuf(2 * NODE_HEADER_SIZE + ind.alignedsize), buf = buf, buf1 = buf, ind0 = ind, keyset(gch) = gc-heap(lpt1, log0), log = log0, lpt = lpt0, m = m0, n0 = 0, n < # avol, awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), log-group-block(log0, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), 0 + ind.flashsize ≤ # buf, m3 + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → m3 = # buf0 ⊦ [encode_index_node#(ind, 0; m, buf; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf1 ∧ subarray(buf, 0, n0) = subarray(buf1, 0, n0) ∧ subarray(buf, n0 + ind0.flashsize, # buf1 - n0 + ind0.flashsize) = subarray(buf1, n0 + ind0.flashsize, # buf1 - n0 + ind0.flashsize) ∧ (err = ESUCCESS → abs-node(subarray(buf, n0, ind0.flashsize), ind0) ∧ m = ind0.flashsize) → ⟪isbuf1 := false; bleb1 := buffered(n); if err = ESUCCESS then if ¬ lpt1[bleb0.leb].size + m ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m0, log0, avol, lpt0, ns, bleb1; ; isbuf1); err := ENOSPC} else {awbuf_write_buf#(m, buf, adr0, m0, log0, lpt0, ns, bleb1; avol, isbuf1; err); if err = ESUCCESS then {adr := @(bleb0.leb, lpt1[bleb0.leb].size, m); lpt1[bleb0.leb] := mklp(lpt1[bleb0.leb].ref-size, lpt1[bleb0.leb].size + m, lpt1[bleb0.leb].flags, lpt1[bleb0.leb].gcheapidx)} else lpt1[bleb0.leb] := mklp(lpt1[bleb0.leb].ref-size, LEB_SIZE, lpt1[bleb0.leb].flags, lpt1[bleb0.leb].gcheapidx)} else {debug#("persistence: could not encode index node"); awbuf_enter_readonly#(adr0, m0, log0, avol, lpt0, ns, bleb1; ; isbuf1)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb1, log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol))

Rule argument

spec: abs-node, inst: encoding-index-node name: encode-node seq: n + ind.flashsize ≤ # buf, buf0 = buf ⊦ ⟪encode_index_node#(ind, n; m, buf; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ subarray(buf, 0, n) = subarray(buf0, 0, n) ∧ subarray (buf, n + ind.flashsize, # buf0 - n + ind.flashsize) = subarray (buf0, n + ind.flashsize, # buf0 - n + ind.flashsize) ∧ ( err = ESUCCESS → abs-node(subarray(buf, n, ind.flashsize), ind) ∧ m = ind.flashsize)) subst: [n, ind, buf, m, err, buf0] → [0, ind, buf, m, err, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ind.flashsize = 2 * NODE_HEADER_SIZE + ind.alignedsize; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # mkbuf(n) = n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)