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Proof step 91 from proof refine-allocate-gnd (previous step)

# lpt = # avol0, # lpt0 = # avol0, lpt[n0] = mklp(0, m3, LP_FREE, m2), keyset(gch) = gc-heap(lpt, log1), log0 = log1, pstate0 = pstate, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate ≠ readonly, ginval < # avol0, n0 < # avol0, abs-gstore(avol0, lpt, gstore, ginval), abs-istore(avol0, lpt, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), synced(avol0), istore0 ⊑ istore, ¬ dups(log1), pstate = unbuffered → bleb = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate ≠ unbuffered → bleb = buffered(pstate.lnum) ⊦ ⟨apersistence_allocate_gnd#(adr0, istore, istore0, gstore0, m, ns0, true; ginval, gstore, log1, pstate; err1)⟩ ( abs-gstore(avol0[n0, mapped(mkbuf(0))], lpt[n0, mklp(0, 0, LP_GROUP_NODES, lpt[n0].gcheapidx)], gstore, ginval) ∧ log1 = log0 + n0 ' ∧ ginval < # avol0 ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ readonly → n0 = pstate.lnum) ∧ ESUCCESS = err1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 92:
# lpt0 = # avol0, # lpt = # avol0, lpt[n0] = mklp(0, m3, LP_FREE, m2), lpt[n0] = mklp(m0, m1, lpf, m4), keyset(gch) = gc-heap(lpt, log1), log0 = log1, pstate0 = pstate, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n0 < # avol0, ginval < # avol0, abs-gstore(avol0, lpt, gstore, ginval), abs-istore(avol0, lpt, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, n0 ' + nx0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), synced(avol0), istore0 ⊑ istore, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb = nobuffer ⊦ ⟨apersistence_allocate_gnd#(adr0, istore, istore0, gstore0, m, ns0, true; ginval, gstore, log1, pstate; err1)⟩ ( abs-gstore(avol0[n0, mapped(mkbuf(0))], lpt[n0, mklp(0, 0, LP_GROUP_NODES, m4)], gstore, ginval) ∧ log1 = log0 + n0 ' ∧ ginval < # avol0 ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ readonly → n0 = pstate.lnum) ∧ ESUCCESS = err1), pstate = readonly, dups(log1)

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt[n0], m0, m1, lpf, m4]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt[n0], m0, m1, lpf, m4