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Proof step 8 from proof inv-get-block-free-size (previous step)

ginval = ginval1, ginval0 = ginval2, gstore = gstore1, gstore0 = gstore2, istore = istore1, istore0 = istore2, btree-inv(rp, adr, istore2, istore1, zh, ri, fi), inv-index(istore2, istore1), inv-journal(nx, gstore2, gstore1, ginval2), inv-state(pstate, nx, gstore2, istore2, syn) ⊦ pstate = unbuffered, ∃ n. n ≤ LEB_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, btree-inv(rp, adr, istore2, istore1, zh, ri, fi), inv(gstore2 \ ginval2), inv(gstore1), inv(istore2), inv(istore1), istore1 ⊑ istore2, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2 ⊦ pstate = unbuffered, dups(nx), ∃ n. n ≤ LEB_SIZE

Rule argument

Additional information

Used simplifier rules: ⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)%⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)%⊦ inv-state(pstate, nx, gstore, istore, syn) ↔ ( pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn); (s)