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Proof step 47 from proof prepost-remove-nonend-blocks (previous step)

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

User applied rule case distinction

And closed the goal!

Rule argument

pos: left 2

Additional information

Used simplifier rules: ⊦ # [] = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ # gndx = 0 ↔ gndx = []; (s)% ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ firstn(n, lax) = [] ↔ n = 0; (s)