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Proof step 38 from proof refine-get-block-free-size (previous step)

# 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)

Heuristic elimination applied rule insert elim lemma

And closed the goal!

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] → [lpt2[n], m, m0, lpf, m1]

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # lpt ⊦ lpt[n] = mklp(n0, n1, lpf, n2) ∧ lpt-leb-size(lpt) → ¬ LEB_SIZE < n1; (s)%⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt2[n], m, m0, lpf, m1