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Proof step 6 from proof nodes-cons-rec (previous step)

gstore[@(m, m0, m1)] = mkgnode(nd0, m2, boolvar, boolvar0) ⊦ nodes-cons(@(m, m0, m1) ' + ax, nd ' + ndx, gstore, ginval) ↔ @(m, m0, m1) ∈ gstore ∧ ¬ m ∈ ginval ∧ nd0 = nd ∧ # ax = # ndx ∧ (∀ n. n < # ax → ax[n] ∈ gstore ∧ ¬ ax[n].lnum ∈ ginval ∧ gstore[ax[n]].nd = ndx[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ nodes-cons(ax, ndx, gstore, ginval) ↔ # ax = # ndx ∧ (∀ n. n < # ax → ax[n] ∈ gstore ∧ ¬ ax[n].lnum ∈ ginval ∧ gstore[ax[n]].nd = ndx[n])
Proof step 8:
gstore[@(m, m0, m1)] = mkgnode(nd0, m2, boolvar, boolvar0) ⊦ #(@(m, m0, m1) ' + ax) = #(nd ' + ndx) ∧ (∀ n. n < #(@(m, m0, m1) ' + ax) → (@(m, m0, m1) ' + ax)[n] ∈ gstore ∧ ¬ (@(m, m0, m1) ' + ax)[n].lnum ∈ ginval ∧ gstore[(@(m, m0, m1) ' + ax)[n]].nd = (nd ' + ndx)[n]) ↔ @(m, m0, m1) ∈ gstore ∧ ¬ m ∈ ginval ∧ nd0 = nd ∧ # ax = # ndx ∧ (∀ n. n < # ax → ax[n] ∈ gstore ∧ ¬ ax[n].lnum ∈ ginval ∧ gstore[ax[n]].nd = ndx[n])

Rule argument

spec: <toplevel> name: nodes-cons seq: ⊦ nodes-cons(ax, ndx, gstore, ginval) ↔ # ax = # ndx ∧ (∀ n. n < # ax → ax[n] ∈ gstore ∧ ¬ ax[n].lnum ∈ ginval ∧ gstore[ax[n]].nd = ndx[n]) subst: [ginval, gstore, ndx, ax] → [ginval, gstore, nd ' + ndx, @(m, m0, m1) ' + ax] flags: <all paths>

Additional information

Used terms: ginval, gstore, nd ' + ndx, @(m, m0, m1) ' + ax