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Proof step 18 from proof prepost-gc-referenced-nodes (previous step)

# lax = # gndx0 + # gndx2 + 1, # ax2 = # gndx2, lax.to-adr(lnum) = ax + adr ' + ax2, gstore2[lnum] = groupblock(gndx0 + gnd ' + gndx2, lax, m), gnd = mkgnode(nd, m0, boolvar, boolvar0), inv(groupblock(gndx0 + gnd ' + gndx2, lax, m)), inv(gstore2 \ ginval), ri-cons(ri, nodes(gstore2 ↓, ginval)), lnum ∈ gstore2 ⊦ ⟪index_index_lookup#(nd.key, ri, fi, ginval, gstore2, gstore, nx, pmaxino, p_os, jvalid0; jvalid, adr0; err); ndx := nodes(gstore2 ↓, ginval)[referenced-adrs(ax, ri)]; if err = ESUCCESS ∧ jvalid ∧ adr0 = adr then ndx := ndx + nd '; ax := adr ' + ax2; gndx1 := gndx0 + gnd ' + gndx2; gndx := gnd ' + gndx2; if err = ESUCCESS then {ax := ax.tail; gndx := gndx.tail}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → (∃ ax0, gndx0. lax.to-adr(lnum) = ax0 + ax ∧ gndx1 = gndx0 + gndx ∧ # ax = # gndx ∧ ndx = nodes(gstore2 ↓, ginval)[referenced-adrs(ax0, ri)])) ∧ ¬ # ax2 < (err = ESUCCESS ⊃ # ax;0)), lnum ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
# ax2 = # gndx2, # lax = # gndx0 + # gndx2 + 1, lax.to-adr(lnum) = ax + adr ' + ax2, gstore2[lnum] = groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax, m), inv(gstore2 \ ginval), inv(groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax, m)), ri-cons(ri, nodes(gstore2 ↓, ginval)), lnum ∈ gstore2, ¬ lnum ∈ ginval ⊦ ⟪index_index_lookup#(nd.key, ri, fi, ginval, gstore2, gstore, nx, pmaxino, p_os, jvalid0; jvalid, adr0; err); ndx := nodes(gstore2 ↓, ginval)[referenced-adrs(ax, ri)]; if err = ESUCCESS ∧ jvalid ∧ adr0 = adr then ndx := ndx + nd '; ax := adr ' + ax2; gndx1 := gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2; gndx := mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2; if err = ESUCCESS then {ax := ax.tail; gndx := gndx.tail}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → (∃ ax0, gndx0. lax.to-adr(lnum) = ax0 + ax ∧ gndx1 = gndx0 + gndx ∧ # ax = # gndx ∧ ndx = nodes(gstore2 ↓, ginval)[referenced-adrs(ax0, ri)])) ∧ ¬ # ax2 < (err = ESUCCESS ⊃ # ax;0))

Rule argument

Additional information

Used simplifier rules: fwd-inv-gblock-rem: ⊦ inv(gstore \ ginval) ∧ n ∈ gstore ∧ ¬ n ∈ ginval ∧ gstore[n] = gblock → inv(gblock); (forward) from specification apersistence-base