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Proof step 37 from proof refine-get-block-free-size (previous step)

# lpt1 = # avol, # lpt2 = # avol, isbuf ↔ pstate = readonly, adr = adr0, bleb0 = bleb1, keyset(gch) = gc-heap(lpt2, log1), log = log1, lpt = lpt1, ns = ns0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb1), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(pstate = readonly, bleb1, lpt2, avol), bufs-log-only(bleb1, log1, lpt2), flash-lpt-cons(lpt1, istore0, gstore0), freelist-cons(lpt2, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt1), lpt-free-unref(lpt2), lpt-leb-size(lpt1), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt1, log1), istore0 ⊑ istore, pstate = unbuffered → isbuf0, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb1 = buffered(pstate.lnum), pstate = unbuffered → bleb1 = nobuffer, isbuf0 → synced(avol) ⊦ bleb0 = nobuffer, dups(log1), LEB_SIZE ≥ lpt2[bleb0.leb].size ∧ bleb0.leb < # lpt2 ∧ bleb0.isbuf?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# lpt1 = # avol, # lpt2 = # avol, keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, LEB_SIZE < lpt2[n].size, n < # avol, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(pstate = readonly, buffered(n), lpt2, avol), bufs-log-only(buffered(n), log1, lpt2), flash-lpt-cons(lpt1, istore0, gstore0), freelist-cons(lpt2, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt1), lpt-free-unref(lpt2), lpt-leb-size(lpt1), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt1, log1), istore0 ⊑ istore, pstate ≠ readonly → n = pstate.lnum, isbuf0 → synced(avol), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore ⊦ pstate = unbuffered, dups(log1)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ buffered(m).leb = m; (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ bleb.isbuf? ↔ (∃ n. bleb = buffered(n)); (as)% ⊦ bleb.isbuf? ↔ bleb ≠ nobuffer; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)