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Proof step 116 from proof refine-allocate-gnd (previous step)

# lpt = # avol0, # lpt0 = # avol0, lpt[n0] = mklp(0, m1, LP_FREE, m4), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol0, n0 < # avol0, abs-gstore(avol0, lpt, gstore, ginval), abs-istore(avol0, lpt, istore2), 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, istore1, gstore0), freelist-cons(lpt, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), 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), istore1 ⊑ istore2, pstate = unbuffered → bleb = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore2, pstate ≠ unbuffered → bleb = buffered(pstate.lnum) ⊦ pstate = readonly, dups(log1), (n < # avol0 ∧ lpt[n0, mklp(0, 0, LP_GROUP_NODES, m4)][n].flags = LP_GROUP_NODES ↔ n ∈ gstore[n0, groupblock([], [], 0)]) ∧ ( n ∈ gstore[n0, groupblock([], [], 0)] ∧ (n = n0 ∨ ¬ n ∈ ginval) → abs-leb(avol0[n0, mapped(mkbuf(0))][n], gstore[n0, groupblock([], [], 0)][n], lpt[n0, mklp(0, 0, LP_GROUP_NODES, m4)][n])) ∧ (n ∈ gstore[n0, groupblock([], [], 0)] → lpt[n0, mklp(0, 0, LP_GROUP_NODES, m4)][n].ref-size = gstore[n0, groupblock([], [], 0)][n].ref-size)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 117:
# lpt0 = # avol0, # lpt = # avol0, lpt[n0] = mklp(0, m1, LP_FREE, m4), gstore[n0, groupblock([], [], 0)][n] = groupblock(gndx, lax, m), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore1) = istore1, 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, istore2), 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, istore1, gstore0), freelist-cons(lpt, n0 ' + nx0), inv(istore1), inv(istore2), 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), istore1 ⊑ istore2, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb = nobuffer ⊦ pstate = readonly, dups(log1), (n < # avol0 ∧ lpt[n0, mklp(0, 0, LP_GROUP_NODES, m4)][n].flags = LP_GROUP_NODES ↔ n ∈ gstore[n0, groupblock([], [], 0)]) ∧ ( n ∈ gstore[n0, groupblock([], [], 0)] ∧ (n = n0 ∨ ¬ n ∈ ginval) → abs-leb(avol0[n0, mapped(mkbuf(0))][n], gstore[n0, groupblock([], [], 0)][n], lpt[n0, mklp(0, 0, LP_GROUP_NODES, m4)][n])) ∧ (n ∈ gstore[n0, groupblock([], [], 0)] → lpt[n0, mklp(0, 0, LP_GROUP_NODES, m4)][n].ref-size = m)

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore[n0, groupblock([], [], 0)][n], gndx, lax, m]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore[n0, groupblock([], [], 0)][n], gndx, lax, m