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Proof step 14 from proof prepost-gc-referenced-nodes (previous step)

# lax = # gndx0 + # gndx, # ax1 = # gndx, lax.to-adr(lnum) = ax + ax1, gstore2[lnum] = groupblock(gndx0 + gndx, lax, m), ax1 = adr + ax2, inv(groupblock(gndx0 + gndx, lax, m)), inv(gstore2 \ ginval), ri-cons(ri, nodes(gstore2 ↓, ginval)), lnum ∈ gstore2 ⊦ ⟪index_index_lookup#(gndx.head.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 + gndx.head.nd '; ax := ax1; gndx1 := gndx0 + gndx; 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)])) ∧ (err = ESUCCESS ⊃ # ax;0) < # ax1), ax1 = [], gndx = [], lnum ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# lax = # gndx0 + # gndx, # ax2 + 1 = # gndx, lax.to-adr(lnum) = ax + adr ' + ax2, gstore2[lnum] = groupblock(gndx0 + gndx, lax, m), gndx ≠ [], inv(gstore2 \ ginval), inv(groupblock(gndx0 + gndx, lax, m)), ri-cons(ri, nodes(gstore2 ↓, ginval)), lnum ∈ gstore2, ¬ lnum ∈ ginval ⊦ ⟪index_index_lookup#(gndx.head.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 + gndx.head.nd '; ax := adr ' + ax2; gndx1 := gndx0 + gndx; 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: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ adr ' + ax ≠ []; (s)% ⊦ m +1 = m + 1; (s)% ⊦ #(adr ' + ax) = (# ax)+1; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ adr + ax = adr ' + ax; (s)