GRACE17 Proof workbench
Local kernel starting…
Game

Playground.g17

Symbols
\forall ∀ · \exists ∃ · \in ∈ · \notin ∉
\to / \imp → · \iff / \lr ↔
\and ∧ · \or ∨ · \not ¬
\powerset 𝒫 · \bigcup ⋃ · \cup ∪ · \cap ∩
\setminus ∖ · \subset ⊆ · \times × · \uplus ⊎
\simeq ≃ · \mapsto ↦ · \quot ⧸ · \int ∫ · \prod ∏ · \sqrt √ · % remainder
u\_n uₙ · a\_1 a₁ · u[n + 1] arbitrary index
\< ⟨ · \> ⟩ for patterns
Type a command, then Space, Tab, or Enter.
Ln 1, Col 1

Save your changes?

has unsaved changes.

Your changes will be lost if you don’t save them.

Search libraries

Cumulus and workspace sources · declarations may be unchecked

Search syntax

Combine words or quoted phrases. Filter by name:, module:, kind:, symbol:, or conclusion:. Prefix a criterion with - to exclude it.

pattern:"?x = ?x" searches conclusions using source tokens; _ matches any balanced expression and repeated ?x must match identically. This is syntactic, not typed matching. For checked goal-directed search, use exact?, apply?, or rw? in a proof.

Open .g17 files or a project folder to include your own libraries. Arrow Down moves to results; Tab moves between actions.

Help

From a first definition to a checked inductive proof. In inference rules, Γ denotes the current local context.

Axiom audit

Grace17 Version

The grace17 proof assistant for
mathematics based on set theory.

Created by Grant Olney Passmore

length([ω, V(ω), 𝒫(V(ω))]) = 3 by compute