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Proof step 5 from proof inv-set-gblock-refsize (previous step)

ginval = ginval1, ginval0 = ginval2, istore = istore1, istore0 = istore2, maxino = maxino1, maxino0 = maxino2, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems nx ∩ ginval2 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval2, btree-inv(rp, adr, istore2, istore1, zh, ri, fi), inv(gstore \ ginval2), inv(gstore0), inv(istore2), inv(istore1), maxino2 ∈ gstore, istore1 ⊑ istore2, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore2, pstate = unbuffered → syn ⊦ ⟪apersistence_set_gblock_refsize#(maxino0, n, adr, istore0, istore, ginval0, gstore0, nx, maxino, ginval, pstate, syn; gstore)⟫ ( inv(gstore \ ginval2) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval2 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore2) ∧ (pstate = unbuffered → syn)), dups(nx)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: apersistence-asm name: inv-set-gblock-refsize seq: inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), inv-state(pstate, nx, gstore, istore, syn), maxino ∈ gstore ⊦ ⟪apersistence_set_gblock_refsize# (maxino, n, adr, istore, istore0, ginval, gstore0, nx, maxino0, ginval0, pstate, syn ; gstore)⟫ ( inv-journal(nx, gstore, gstore0, ginval) ∧ inv-state(pstate, nx, gstore, istore, syn)) subst: [syn, pstate, ginval0, maxino0, nx, gstore0, ginval, istore0, istore, adr, n, maxino, gstore] → [syn, pstate, ginval, maxino, nx, gstore0, ginval0, istore, istore0, adr, n, maxino0, gstore] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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)%⊦ 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-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)