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Proof step 17 from proof nodes-cons-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# ax = # ndx, gstore[@(m, m0, m1)] = mkgnode(nd, m2, boolvar, boolvar0), @(m, m0, m1) ∈ gstore, n ≤ # ndx, ∀ n. n < # ndx → ax[n] ∈ gstore ∧ ¬ ax[n].lnum ∈ ginval ∧ gstore[ax[n]].nd = ndx[n] ⊦ m ∈ ginval, (@(m, m0, m1) ' + ax)[n] ∈ gstore ∧ ¬ (@(m, m0, m1) ' + ax)[n].lnum ∈ ginval ∧ gstore[(@(m, m0, m1) ' + ax)[n]].nd = (nd ' + ndx)[n]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)