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Proof step 6 from proof inv-add-gnds (previous step)

ginval = ginval1, ginval0 = ginval2, istore = istore1, istore0 = istore2, pstate = journal(nx.last), 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), inv(gstore[nx.last]), nx.last ∈ gstore, istore1 ⊑ istore2 ⊦ ⟪if nx ≠ [] ∧ pstate.journal? then apersistence_add_gnds#(adr, istore0, istore, ginval0, gstore0, nx, maxino, ginval; gndx, ax, gstore, pstate, syn; err) else abort⟫ ( inv(gstore \ ginval2) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval2 ∧ (pstate.journal? → pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore2) ∧ (pstate = unbuffered → syn)), nx = [], dups(nx)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 7:
ginval = ginval1, ginval0 = ginval2, istore = istore1, istore0 = istore2, pstate = journal(nx.last), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval2 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval2, btree-inv(rp, adr, istore2, istore1, zh, ri, fi), inv(gstore[nx.last]), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval2), nx.last ∈ gstore, istore1 ⊑ istore2 ⊦ ⟪apersistence_add_gnds#(adr, istore0, istore, ginval0, gstore0, nx, maxino, ginval; gndx, ax, gstore, pstate, syn; err)⟫ ( inv(gstore \ ginval2) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval2 ∧ (pstate.journal? → pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore2) ∧ (pstate = unbuffered → syn)), nx = [], dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ journal(m).journal?; (s)