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Proof step 48 from proof prepost-gc-referenced-nodes (previous step)

# gndx0 = # lax1, # lax = # gndx2, ri[nd.key] = @(m1, m2, m3), gstore2[m1] = groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m), inv(gstore2 \ ginval), inv(groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m)), ri-cons(ri, nodes(gstore2 ↓, ginval)), nd.key ∈ ri, m1 ∈ gstore2, @(m1, m2, m3) ∈ nodes(gstore2 ↓, ginval) ⊦ nd = gstore2 ↓[@(m1, m2, m3)].nd, m1 ∈ ginval

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 49:
# lax = # gndx2, # gndx0 = # lax1, gstore2[m1] = groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m), ri[nd.key] = @(m1, m2, m3), gstore2 ↓[@(m1, m2, m3)] = mkgnode(nd0, m4, boolvar1, boolvar2), inv(groupblock(gndx0 + mkgnode(nd, m0, boolvar, boolvar0) ' + gndx2, lax1 + @(m2, m3) ' + lax, m)), inv(gstore2 \ ginval), ri-cons(ri, nodes(gstore2 ↓, ginval)), @(m1, m2, m3) ∈ nodes(gstore2 ↓, ginval), m1 ∈ gstore2, nd.key ∈ ri ⊦ nd = nd0, m1 ∈ 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] → [gstore2 ↓[@(m1, 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: gstore2 ↓[@(m1, m2, m3)], nd0, m4, boolvar1, boolvar2