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Proof step 44 from proof prepost-remove-nonend-blocks (previous step)

# lax = (# gndx0 + 1) + # gndx, gstore2[n] = groupblock((gndx0 + mkgnode(nd, m1, boolvar, false) ') + gndx, lax, m), prefixn(# gndx0 + 1, lax) = [], 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 ⊦ ax0.butlast = ax0 + prefixn(# gndx0, lax).to-adr(n), ax0 = [], n ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ prefixn(n, lax) = (n ≤ # lax ⊃ firstn(n, lax);lax)
Proof step 46:
# lax = (# gndx0 + 1) + # gndx, (# gndx0 + 1 ≤ # lax ⊃ firstn(# gndx0 + 1, lax);lax) = [], 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.butlast = ax0 + prefixn(# gndx0, lax).to-adr(n), ax0 = [], n ∈ ginval

Rule argument

spec: list-prefixn, inst: laddress-list name: prefixn seq: ⊦ prefixn(n, lax) = (n ≤ # lax ⊃ firstn(n, lax);lax) subst: [lax, n] → [lax, # gndx0 + 1] flags: <all paths>

Additional information

Used terms: lax, # gndx0 + 1