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Proof step 32 from proof nodes-write-same-flushed (previous step)

gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][@(m, m2, m3)] = mkgnode(nd, m1, boolvar, boolvar0), gstore[m] = groupblock(gndx, lax, n0), m ∈ gstore, @(m2, m3) ∈ prefixn(valid-group-nodes(gndx), lax), valid-group-nodes(gndx) ≤ n0, n0 ≤ m0, valid-group-nodes(gndx) ≤ m0 ⊦ nd = gstore ↓[@(m, m2, m3)].nd, m ∈ ginval

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
gstore[m] = groupblock(gndx, lax, n0), gstore ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0)][@(m, m2, m3)] = mkgnode(nd, m1, boolvar, boolvar0), gstore ↓[@(m, m2, m3)] = mkgnode(nd0, m4, boolvar1, boolvar2), @(m2, m3) ∈ prefixn(valid-group-nodes(gndx), lax), m ∈ gstore, valid-group-nodes(gndx) ≤ m0, n0 ≤ m0, valid-group-nodes(gndx) ≤ n0 ⊦ nd = nd0, m ∈ ginval

Rule argument

spec: groupnode name: elim seq: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0) subst: [gnd, nd, m, boolvar, boolvar0] → [gstore ↓[@(m, m2, m3)], nd0, m4, boolvar1, boolvar2]

Additional information

Used simplifier rules: ⊦ ((nd = gnd.nd ∧ m = gnd.sqnum) ∧ (boolvar ↔ gnd.start)) ∧ (boolvar0 ↔ gnd.end) ↔ gnd = mkgnode(nd, m, boolvar, boolvar0); (elim) Used terms: gstore ↓[@(m, m2, m3)], nd0, m4, boolvar1, boolvar2