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Proof step 129 from proof refine-allocate-ind (previous step)

# lpt2 = # avol0, # lpt0 = # avol0, lpt2[n0] = mklp(0, m5, LP_FREE, m6), keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol0, n0 < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), istore0 ⊑ istore, 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), bleb ≠ buffered(n0) → ( bleb ≠ nobuffer → avol0[n0, mapped(mkbuf(0))][bleb.leb].mapped? ∧ bleb.leb < # avol0[n0, mapped(mkbuf(0))] ∧ n0 < # avol0 ∧ bleb.isbuf?) ∧ ( bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE) → (n0 < # avol0[n0, mapped(mkbuf(0))] ∧ n0 < # avol0) ∧ ( avol0[n0, mapped(mkbuf(0))][n0].mapped? → avol0[n0, mapped(mkbuf(0))][n0].mapped? ∧ n0 < # avol0[n0, mapped(mkbuf(0))] ∧ n0 < # avol0)) ⊦ bleb = buffered(n0), pstate = readonly, dups(log1), (bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE)) ∧ avol0[n0, mapped(mkbuf(0))][n0].mapped? ∧ avol0[n0, mapped(mkbuf(0))][n0].data = mkbuf(0)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ n < # avol ∧ synced(avol) ∧ avol[n] = mapped(buf) → is-aligned(# buf, EB_PAGE_SIZE); (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%m ≠ n ⊦ avol[m, aleb][n] = avol[n]; (s)% ⊦ buffered(m).leb = m; (s)% ⊦ bleb.isbuf? ↔ (∃ n. bleb = buffered(n)); (as)% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ # avol[n, aleb] = # avol; (s)