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Proof step 3 from proof nodes-append-subseteq (previous step)

# gndx = # lax, gstore[n] = groupblock(gndx, lax, n0), n ∈ gstore, n0 ≤ m0 ⊦ nodes(gstore ↓, ginval) ⊆ nodes (gstore ↓ [n, groupblock (prefixn((gnd.end ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + gnd '), prefixn((gnd.end ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ fs ⊆ fs0 ↔ (∀ adr. adr ∈ fs → adr ∈ fs0 ∧ fs[adr] = fs0[adr])
Proof step 5:
# gndx = # lax, gstore[n] = groupblock(gndx, lax, n0), n ∈ gstore, n0 ≤ m0 ⊦ ∀ adr. adr ∈ nodes(gstore ↓, ginval) → adr ∈ nodes (gstore ↓ [n, groupblock (prefixn((gnd.end ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + gnd '), prefixn((gnd.end ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval) ∧ nodes(gstore ↓, ginval)[adr] = nodes (gstore ↓ [n, groupblock (prefixn((gnd.end ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + gnd '), prefixn((gnd.end ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval) [adr ]

Rule argument

spec: store, inst: node-store name: Subset seq: ⊦ fs ⊆ fs0 ↔ (∀ adr. adr ∈ fs → adr ∈ fs0 ∧ fs[adr] = fs0[adr]) subst: [fs0, fs] → [nodes (gstore ↓ [n, groupblock (prefixn ((gnd.end ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + gnd '), prefixn ((gnd.end ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval), nodes(gstore ↓, ginval)] flags: <all paths>

Additional information

Used terms: nodes (gstore ↓ [n, groupblock (prefixn ((gnd.end ⊃ # lax + 1;valid-group-nodes(gndx)), gndx + gnd '), prefixn ((gnd.end ⊃ # lax + 1;valid-group-nodes(gndx)), lax + ladr '), m0) ], ginval), nodes(gstore ↓, ginval)