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Proof step 112 from proof refine-add-gnds (previous step)

# gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore1 ∪ ginval, gstore1[n] = groupblock(gndx1, lax1, m0), avol[n] = mapped(buf), lpt1[n] = mklp(m0, m1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, nx + n '), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval ∩ elems nx = ∅, gndx0 ≠ [], lax0 ≠ [], LEB_SIZE < m1 + gndx0.flashsize, ginval < # avol, n < # avol, abs-gstore(avol, lpt1, gstore1, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, m1, gndx0, lax0, false), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx1, lax1, m0)), inv(gstore1 \ ginval), inv(gstore0), inv(istore2), inv(istore1), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore1, istore1 ⊑ istore2, ¬ dups(nx), ¬ n ∈ nx, ¬ n ∈ ginval, isbuf1 → synced(avol) ⊦ ∃ ax. ⟨isbuf1 := ?⟩ ( abs-gstore(avol, lpt1, gstore1[n, (gstore1[n].gndlist:= gstore1[n].gndlist).ladrlist:= gstore1[n].ladrlist], ginval) ∧ (isbuf1 → synced(avol)) ∧ lax0.to-adr(n) = ax)

User applied rule exists right

And obtained the following new goals

Proof step 113:
# lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, (elems nx ∪ dom gstore0) ++ n = dom gstore1 ∪ ginval, lpt1[n] = mklp(m0, m1, LP_GROUP_NODES, m2), avol[n] = mapped(buf), gstore1[n] = groupblock(gndx1, lax1, m0), keyset(gch) = gc-heap(lpt1, nx + n '), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, n < # avol, ginval < # avol, LEB_SIZE < m1 + gndx0.flashsize, abs-gstore(avol, lpt1, gstore1, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, m1, gndx0, lax0, false), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore0), inv(gstore1 \ ginval), inv(groupblock(gndx1, lax1, m0)), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore1, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ ⟨isbuf1 := ?⟩ ( abs-gstore(avol, lpt1, gstore1[n, (gstore1[n].gndlist:= gstore1[n].gndlist).ladrlist:= gstore1[n].ladrlist], ginval) ∧ (isbuf1 → synced(avol)) ∧ lax0.to-adr(n) = lax0.to-adr(n)), gndx0 = [], lax0 = [], dups(nx), n ∈ nx, n ∈ ginval

Rule argument

pos: right 1 terms: lax0.to-adr(n) abort: F discard: T computed: T

Additional information

Used terms: lax0.to-adr(n)