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Proof step 10 from proof inv-get-gc-block (previous step)

# lpt = # avol, keyset(gch) = gc-heap(lpt, log), gch.size ≠ 0, bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf, bleb, lpt, avol), bufs-log-only(bleb, log, lpt), freelist-cons(lpt, freelist), log-group-block(log, lpt), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log), ¬ dups(log) ⊦ ⟪gc_heap_get_min#(gch; n); err := ESUCCESS⟫ ((err = ENOSPC ∨ err = ESUCCESS) ∧ (err ≠ ESUCCESS → n = n0) ∧ (err = ESUCCESS → n < # avol ∧ lpt[n].flags = LP_GROUP_NODES ∧ ¬ n ∈ log))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
# lpt = # avol, gch = bin-heap(kar, m), keyset(gch) = gc-heap(lpt, log), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf, bleb, lpt, avol), bufs-log-only(bleb, log, lpt), freelist-cons(lpt, freelist), log-group-block(log, lpt), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log) ⊦ ⟪gc_heap_get_min#(gch; n); err := ESUCCESS⟫ ((err = ENOSPC ∨ err = ESUCCESS) ∧ (err ≠ ESUCCESS → n = n0) ∧ (err = ESUCCESS → n < # avol ∧ lpt[n].flags = LP_GROUP_NODES ∧ ¬ n ∈ log)), m = 0, dups(log)

Rule argument

spec: bin-min-heap name: elim seq: ⊦ kar = bh.ar ∧ m = bh.size ↔ bh = bin-heap(kar, m) subst: [bh, kar, n] → [gch, kar, n0]

Additional information

Used simplifier rules: ⊦ kar = bh.ar ∧ m = bh.size ↔ bh = bin-heap(kar, m); (elim) Used terms: gch, kar, n0