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Proof step 47 from proof refine-add-ind (previous step)

# lpt1 = # avol, # lpt0 = # avol, istore[m0] = indexblock(indx, lax, m4), lpt1[m0] = mklp(m4, m3, LP_INDEX_NODES, m2), avol[m0] = mapped(buf0), buf = mkbuf(2 * NODE_HEADER_SIZE + ind.alignedsize), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, m0 < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(m0)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(m0), lpt1, avol), bufs-log-only(buffered(m0), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(indexblock(indx, lax, m4)), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), m0 ∈ istore, istore0 ⊑ istore, ¬ dups(log1), m3 + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → m3 = # buf0, isbuf1 → synced(avol) ⊦ [encode_index_node#(ind, 0; m1, buf; err); adr := adr2; isbuf2 := false; bleb1 := buffered(m0); if err = ESUCCESS then if ¬ lpt1[buffered(m0).leb].size + m1 ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb1; ; isbuf2); err := ENOSPC} else {awbuf_write_buf#(m1, buf, adr0, m, log1, lpt0, ns0, bleb1; avol, isbuf2; err); if err = ESUCCESS then {adr := @(buffered(m0).leb, lpt1[buffered(m0).leb].size, m1); lpt1[buffered(m0).leb] := mklp (lpt1[buffered(m0).leb].ref-size, lpt1[buffered(m0).leb].size + m1, lpt1[buffered(m0).leb].flags, lpt1[buffered(m0).leb].gcheapidx)} else lpt1[buffered(m0).leb] := mklp(lpt1[buffered(m0).leb].ref-size, LEB_SIZE, lpt1[buffered(m0).leb].flags, lpt1[buffered(m0).leb].gcheapidx)} else {debug#("persistence: could not encode index node"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb1; ; isbuf2)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(bleb1, log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol → ⟨pstate := index(m0); apersistence_add_ind#(ind, adr0, istore0, ginval, gstore, gstore0, log1, m, ns0; adr2, istore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb1 = nobuffer) ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb1 = buffered(pstate.lnum)) ∧ adr = adr2 ∧ err = err0))

User applied rule insert program lemma

And obtained the following new goals

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, m1, 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)