Commit 4b6470e
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feat(Dijkstra/Ledger/PoV): prove SUBLEDGERS-utxo-coin
Proves by induction on the SUBLEDGERS transition that the UTxO-state
coin total at the start of a sub-tx batch plus all outs + donations
equals the UTxO coin total at the end plus all consumed spend inputs
(compared against the batch-start snapshot `utxo₀`):
```agda
getCoin (UTxOStateOf s₀) + Σ (cbalance (outs stx) + DonationsOf stx)
≡ getCoin (UTxOStateOf s₁) + Σ cbalance (utxo₀ ∣ SpendInputsOf stx)
```
Base case (`BS-base Id-nop`): both sides reduce to `x + 0`, so `refl`.
Inductive case: `SUBLEDGER-I` is impossible under `isTopLevelValid ≡
true`; `SUBLEDGER-V` combines the per-step SUBUTXOW balance with the
IH via an eight-step +-commutative-monoid rearrangement.
Introduces `subutxow-step-coin` as a new module parameter:
```agda
getCoin s₀ + cbalance (outs stx) + DonationsOf stx
≡ getCoin s₁ + cbalance (UTxOOf Γ ∣ SpendInputsOf stx)
```
+ Rationale for keeping this as a parameter at the SUBLEDGERS level:
proving it locally requires, beyond `balance-∪` and `split-balance`,
two batch-wide invariants:
1. the running UTxO agrees with `utxo₀` on every sub-tx's spend
inputs, and
2. freshness of each sub-tx's TxId relative to the running UTxO
neither of which is a local SUBUTXO premise; both follow from
batch-wide disjointness exposed by the outer UTXO rule and will be
discharged in a follow-up PR dedicated to general Dijkstra PoV
infrastructure.
Statement parallels the existing `SUBLEDGERS-certs-pov`, uses
`SubLedgerEnv.utxo₀ Γ` uniformly on the RHS (matching the shape of
`batch-balance-coin`), and is the key lemma needed to derive
`batch-utxo-accounting` internally in the next step of this PR.1 parent e0d513e commit 4b6470e
4 files changed
Lines changed: 480 additions & 273 deletions
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- src/Ledger/Dijkstra/Specification
- Ledger/Properties
- Utxow/Properties
- Utxo/Properties
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