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Proof step 35 from proof refine-get-block-free-size (previous step)

# lpt2 = # avol, # lpt1 = # avol, LEB_SIZE = n1 + m1, lpt2[n2] = mklp(m0, m1, lpf, m2), keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol, n2 < # avol, abs-gstore(avol, lpt2, gstore2, ginval), abs-istore(avol, lpt2, istore2), awbuf-inv(avol, buffered(n2)), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(pstate = readonly, buffered(n2), lpt2, avol), bufs-log-only(buffered(n2), log1, lpt2), flash-lpt-cons(lpt1, istore1, gstore1), freelist-cons(lpt2, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt1), lpt-leb-size(lpt1), lpt-ram-flash(lpt2, lpt1, log1), m1 ≤ LEB_SIZE, istore1 ⊑ istore2, pstate ≠ readonly → n2 = pstate.lnum, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, isbuf0 → synced(avol), pstate.lnum < # avol → lpt2[pstate.lnum].size ≤ LEB_SIZE ⊦ n1 ≤ LEB_SIZE ∧ ⟨n0 := n1⟩ ((isbuf0 → synced(avol)) ∧ (pstate ≠ readonly → n2 = pstate.lnum) ∧ n1 = n0), pstate = unbuffered, dups(log1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# lpt2 = # avol, # lpt1 = # avol, LEB_SIZE = n1 + m1, lpt2[n2] = mklp(m0, m1, lpf, m2), keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, pstate ≠ unbuffered, ginval < # avol, n2 < # avol, abs-gstore(avol, lpt2, gstore2, ginval), abs-istore(avol, lpt2, istore2), awbuf-inv(avol, buffered(n2)), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(pstate = readonly, buffered(n2), lpt2, avol), bufs-log-only(buffered(n2), log1, lpt2), flash-lpt-cons(lpt1, istore1, gstore1), freelist-cons(lpt2, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt1), lpt-leb-size(lpt1), lpt-ram-flash(lpt2, lpt1, log1), m1 ≤ LEB_SIZE, n1 ≤ LEB_SIZE, istore1 ⊑ istore2, ¬ dups(log1), pstate ≠ readonly → n2 = pstate.lnum, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, isbuf0 → synced(avol), pstate.lnum < # avol → lpt2[pstate.lnum].size ≤ LEB_SIZE ⊦ ⟨n0 := n1⟩ ((isbuf0 → synced(avol)) ∧ (pstate ≠ readonly → n2 = pstate.lnum) ∧ n1 = n0)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)