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Proof step 53 from proof prepost-remove-nonend-blocks (previous step)

# lax = (# gndx0 + 1) + # gndx, gstore2[n] = groupblock((gndx0 + mkgnode(nd, m1, boolvar, false) ') + gndx, lax, m), valid-group-nodes(gndx0) = valid-group-nodes((gndx0 + mkgnode(nd, m1, boolvar, false) ') + gndx), inv(gstore2 \ ginval), inv(groupblock((gndx0 + mkgnode(nd, m1, boolvar, false) ') + gndx, lax, m)), n ∈ gstore2 ⊦ ax0 + prefixn(# gndx0 + 1, lax.to-adr(n)) = [], prefixn(# gndx0 + 1, lax.to-adr(n)).butlast = prefixn(# gndx0, lax).to-adr(n), lax = [], n ∈ ginval, # gndx0 + 1 ≠ 0 ∧ # gndx0 + 1 ≤ # lax.to-adr(n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
# lax = (# gndx0 + 1) + # gndx, gstore2[n] = groupblock((gndx0 + mkgnode(nd, m1, boolvar, false) ') + gndx, lax, m), valid-group-nodes(gndx0) = valid-group-nodes((gndx0 + mkgnode(nd, m1, boolvar, false) ') + gndx), inv(groupblock((gndx0 + mkgnode(nd, m1, boolvar, false) ') + gndx, lax, m)), inv(gstore2 \ ginval), n ∈ gstore2, # lax ≤ # gndx0 ⊦ ax0 + lax.to-adr(n) = [], (lax.to-adr(n)).butlast = lax.to-adr(n), lax = [], n ∈ ginval

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%# lax ≤ m ⊦ prefixn(m, lax) = lax; (s)% ⊦ ¬ m < n → ¬ m + m0 < n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ # lax.to-adr(n) = # lax; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)% ⊦ prefixn(n, lax.to-adr(m)) = prefixn(n, lax).to-adr(m); (s)