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Proof step 40 from proof nodes-crash-down (previous step)

gndx0[pos(@(m0, m1), lax0)] = mkgnode(nd, m4, boolvar, boolvar0), gstore ↓[@(m, m0, m1)] = mkgnode(nd0, m3, boolvar1, boolvar2), gstore[m] = groupblock(gndx, lax, m2), crash(gstore, gstore0, ginval, nx) ↓[m] = groupblock(gndx0, lax0, m5), inv(groupblock(gndx, lax, m2)), inv(gstore \ ginval), @(m0, m1) ∈ lax0, m ∈ gstore, @(m0, m1) ∈ prefixn(valid-group-nodes(gndx), lax) ⊦ nd = nd0, m ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓
Proof step 42:
gstore[m] = groupblock(gndx, lax, m2), gstore ↓[@(m, m0, m1)] = mkgnode(nd0, m3, boolvar1, boolvar2), gndx0[pos(@(m0, m1), lax0)] = mkgnode(nd, m4, boolvar, boolvar0), crash(gstore, gstore0, ginval, nx)[m] ↓ = groupblock(gndx0, lax0, m5), inv(gstore \ ginval), inv(groupblock(gndx, lax, m2)), @(m0, m1) ∈ prefixn(valid-group-nodes(gndx), lax), m ∈ gstore, @(m0, m1) ∈ lax0, m ∈ crash(gstore, gstore0, ginval, nx) ⊦ nd = nd0, m ∈ ginval

Rule argument

spec: <toplevel> name: down-store-at seq: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓ subst: [n, gstore] → [m, crash(gstore, gstore0, ginval, nx)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ crash(gstore, gstore0, ginval, nx) ↔ n ∈ gstore ∨ n ∈ ginval; (ws) Used terms: m, crash(gstore, gstore0, ginval, nx)