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Proof step 22 from proof nodes-append-subseteq (previous step)

# gndx = # lax, gstore[n] = groupblock(gndx, lax, n0), gstore ↓[@(n, m1, m2)] = mkgnode(nd0, m, boolvar1, boolvar2), @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax), n ∈ gstore, n0 ≤ m0 ⊦ n ∈ ginval, nd0 = nodes (gstore ↓ [n, groupblock (prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval) [@(n, m1, m2) ] ∧ @(m1, m2) ∈ prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd
Proof step 24:
# gndx = # lax, gstore ↓[@(n, m1, m2)] = mkgnode(nd0, m, boolvar1, boolvar2), gstore[n] = groupblock(gndx, lax, n0), n ∈ gstore, @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax), n0 ≤ m0 ⊦ n ∈ ginval, @(n, m1, m2) ∈ nodes (gstore ↓ [n, groupblock (prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval), nd0 = nodes (gstore ↓ [n, groupblock (prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval) [@(n, m1, m2) ] ∧ @(m1, m2) ∈ prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr ')
Proof step 29:
# gndx = # lax, gstore ↓[@(n, m1, m2)] = mkgnode(nd0, m, boolvar1, boolvar2), gstore[n] = groupblock(gndx, lax, n0), n ∈ gstore, @(m1, m2) ∈ prefixn(valid-group-nodes(gndx), lax), @(n, m1, m2) ∈ nodes (gstore ↓ [n, groupblock (prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval), n0 ≤ m0 ⊦ n ∈ ginval, nd0 = gstore ↓ [n, groupblock (prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ] [@(n, m1, m2) ] .nd ∧ @(m1, m2) ∈ prefixn((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr ')

Rule argument

spec: <toplevel> name: nodes-gstore-at seq: ⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd subst: [adr, ginval, gstore] → [@(n, m1, m2), ginval, gstore ↓ [n, groupblock (prefixn ((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn ((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ]] flags: <all paths>

Additional information

Used terms: @(n, m1, m2), ginval, gstore ↓ [n, groupblock (prefixn ((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + mkgnode(nd, m3, boolvar, boolvar0) '), prefixn ((boolvar0 ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ]