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Proof step 68 from proof inv-recover (previous step)

# lpt3 = # avol0, # avol = # avol0, # lpt2 = # avol0, # avol2 = # avol0, gc-heap(replay-lpt(replay-log(lpt3, log2), log2, # avol0), log2) = keyset(gch), keyset(gch1) = gc-heap(lpt2, log2), avol-replay-lpt-unchanged(avol, avol2, replay-log(lpt3, log2), log2), awbuf-inv(avol2, nobuffer), awbuf-inv(avol0, bleb1), bin-heap-inv(gch1, lpt2), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf1, bleb1, lpt2, avol0), bufs-log-only(bleb1, log2, lpt2), freelist-cons(lpt2, log5), freelist-cons(replay-lpt(replay-log(lpt3, log2), log2, # avol0), freelist), id-idx(replay-lpt(replay-log(lpt3, log2), log2, # avol0), lpt), log-group-block(log2, lpt2), log-group-block(log2, replay-lpt(replay-log(lpt3, log2), log2, # avol0)), lpt-free-unref(lpt2), lpt-free-unref(lpt3), lpt-leb-size(lpt2), lpt-leb-size(lpt3), lpt-ram-flash(lpt2, lpt3, log2), synced(avol0), synced(avol), valid-indices(lpt3, log2), avol ↓ avol0 ⊦ # lpt = # avol0, dups(log2)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: index-array, inst: gc-heap-base name: id-idx seq: ⊦ id-idx(lpt1, lpt0) ↔ # lpt0 = # lpt1 ∧ (∀ n. n < # lpt0 → lpt1[n].ref-size = lpt0[n].ref-size ∧ lpt1[n].size = lpt0[n].size ∧ lpt1[n].flags = lpt0[n].flags) subst: [lpt0, lpt1] → [lpt, replay-lpt(replay-log(lpt3, log2), log2, # avol0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # replay-log(lpt, nx) = # lpt; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ n < n; (s)%n ≤ # lpt ⊦ # replay-lpt(lpt, nx, n) = # lpt; (s) Used terms: lpt, replay-lpt(replay-log(lpt3, log2), log2, # avol0)