「proof」の検索結果

Publish, read, comment on, or edit markdown in Proof. Use for Proof links, sharing specs/plans/drafts, or publish handoffs from planning workflows; avoid proofread, math, evidence, or proof-of-concept meanings.

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Convert an existing prose, flat, or loosely organized mathematical proof into a source-mapped Lamport-style hierarchy without repairing or completing its mathematics. Use when a submitted proof needs a traceable hierarchical rendering before a forward Lamport audit or for clearer presentation. Do not use to invent a proof, certify validity, or restructure an already hierarchical proof merely to audit it.

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Use when the user asks to "build a story bank", "collect our origin and customer stories", or "assemble reusable proof stories for the message"; assembles reusable narrative units — origin, founder, customer, transformation, and proof stories — each tagged to a claims-ledger ID and a message-house pillar, with every proof labeled Measured / User-provided / [needs source]. Not for authoring the message house or pillars — use message-system-architect; not for brand voice or naming rules — use brand-language-codifier; not for finished long-form prose — use content-writer; not for adjudicating whether a proof is true — use offer-claims-registry. 品牌故事库/起源客户转化/证据故事单元

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Build the deterministic PIL pill overlays for a 'perfect-score + proof-points' UGC video ad (white 10/10 score header with a medal + orange sub with a finger-down + 3-4 green-check proof pills) and composite them onto a base clip in a diagonal L->R->L->R cascade, then mux the music bed into master-final.mp4. Config-driven (config.json), 1080x1920 9:16, FREE and deterministic (no paid calls, text stays pixel-crisp). Use for the overlay-proof-points format; the base clip + music come from separate paid capabilities.

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Analyze proof states in Isabelle or Coq and suggest applicable tactics to make progress. Use when users need help with: (1) Choosing the next tactic in an interactive proof, (2) Understanding what tactics apply to their current goal, (3) Getting unstuck in a proof, (4) Learning which tactics work for specific goal structures (conjunctions, implications, induction, etc.). Provides 3-5 ranked tactic suggestions with explanations for intermediate-level proofs in both Isabelle/Isar and Coq.

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Restructure and improve Isabelle or Coq proofs to enhance readability, modularity, and maintainability without changing semantics. Use when proofs are long and monolithic, have repeated patterns, use unclear naming, lack documentation, or when the user asks to refactor, clean up, improve, or reorganize their formal proofs.

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Debug proof failures using counterexamples from Nitpick (Isabelle) or QuickChick (Coq) to identify specification errors, missing preconditions, and proof strategy issues. Use when: (1) A proof attempt fails and you need to understand why, (2) Counterexamples are generated by Nitpick or QuickChick, (3) Specifications may be incorrect or incomplete, (4) Theorems need validation before proving, (5) Missing preconditions or lemmas need identification, or (6) Proof failures need explanation and correction suggestions. Supports both Isabelle/HOL and Coq equally.

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Submit proof requests on the Boundless ZK proof marketplace. Covers wallet setup, CLI configuration, building or discovering guest programs, self-hosting via Cloudflare Quick Tunnels (no Pinata/S3 needed), submitting, and retrieving results. Use when a developer wants to request a ZK proof, submit a proof request, get started with Boundless, try Boundless, or learn the requestor workflow.

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Edits existing marketing copy in ordered passes (structure, claims, sentences, consistency, proof) and returns the edited text with a change log and a list of questions for the author. Flags claims that need evidence instead of inventing proof, and keeps the writer's voice. Use when someone says "edit this copy", "proofread this page", "tighten this", "polish this email", "review my landing page copy", "make this clearer", "check this before we publish", or asks for copy feedback on a page, ad, email or product description.

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Proof writing and verification techniques for mathematical reasoning. Covers 13 proof strategies with canonical worked examples — direct, contrapositive, contradiction, cases, WLOG, vacuous/trivial, biconditional, counterexample, existence (constructive and non-constructive), uniqueness, induction (weak, strong, structural), pigeonhole/double-counting, and diagonal argument/invariants. Use when writing, verifying, or selecting proof strategies for any mathematical claim.

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Fix missing theorem proof terms when analyzing Lean 4 environments via importModules. Use when: (1) ConstantInfo.value? returns none for theorems despite TheoremVal.value being Expr, (2) building code graph / dependency extractor for Lean 4 and getting 0 proof dependency edges, (3) Lean 4.30+ project where theorem proofs appear missing from loaded environment, (4) analyzing Mathlib or any Lean 4 project and proof terms are empty. Root cause: breaking change in Lean 4.30 — value? treats theorems as opaque by default.

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Record, compose, publish, serve, and review short desktop validation video proofs for Pulp UX/test-harness work. Use when the user asks to "show me it working", record a validation video, prove a click/interaction, share a local proof link, attach a video to a review issue, or compare an implemented UI against source material. Covers macOS desktop capture, Remotion proof composition, attachment budgets, local/Tailscale serving, and review closure.

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Verify and write proofs using the Acorn theorem prover for mathematical and cryptographic formalization. Use when working with Acorn proof files (.ac), verifying theorems, formalizing mathematical or cryptographic protocols, or writing proofs in the Acorn language. Triggers on: (1) Creating or editing .ac files, (2) Running acorn verify commands, (3) Formalizing math or crypto proofs, (4) Questions about Acorn syntax or standard library.

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Formally verify programs by writing Lean 4 proofs. Trigger this skill whenever the user wants to formally verify code, generate Lean 4 proofs, prove properties about algorithms or smart contracts, verify invariants, convert program logic into formal specifications, or anything involving Lean 4 and formal verification. Also trigger when the user mentions "qedgen", "lean proof", "formal proof", "verify my code", "prove correctness", "formal verification", or wants mathematical guarantees about their implementation.

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Use when the user asks to "build a story bank", "collect our origin and customer stories", or "assemble reusable proof stories for the message"; assembles reusable narrative units — origin, founder, customer, transformation, and proof stories — each tagged to a claims-ledger ID and a message-house pillar, with every proof labeled Measured / User-provided / [needs source]. Not for authoring the message house or pillars — use message-system-architect; not for brand voice or naming rules — use brand-language-codifier; not for finished long-form prose — use content-writer; not for adjudicating whether a proof is true — use offer-claims-registry. 品牌故事库/起源客户转化/证据故事单元

日本語の概要は準備中です。原文の説明を表示しています。

Audit whether a "current product focus receipt" (Decision/Now/Why-now/Evidence/Not-now/Cut-suspend/First-visible-proof/ Acceptance-gate/Kill-revisit-trigger/Owner/Review-date) and the work order it gates state a real, testable decision and a real agent launch — not planning-placeholder prose that sounds like an assignment but can't be proven. Use when deciding whether to launch an agent chain against a milestone or a stated "focus," when a work order lacks explicit input/output/owner/proof-gate, or when an acceptance gate would only prove a cached UI state instead of daemon truth. NOT for distinguishing roadmap items from energy-driven sidequests (legible-roadmap-with-sidequests), reviewing a PRD/prototype for product-completeness gaps like cold start or pricing (product-reality-reviewer), or accepting already-finished work against a personal acceptance bar (port-daddy-user-surrogate-pm-review).

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Solve competition math problems (IMO, Putnam, USAMO, AIME) with adversarial verification that catches the errors self-verification misses. Activates when asked to 'solve this IMO problem', 'prove this olympiad inequality', 'verify this competition proof', 'find a counterexample', 'is this proof correct', or for any problem with 'IMO', 'Putnam', 'USAMO', 'olympiad', or 'competition math' in it. Uses pure reasoning (no tools) — then a fresh-context adversarial verifier attacks the proof using specific failure patterns, not generic 'check logic'. Outputs calibrated confidence — will say 'no confident solution' rather than bluff. If LaTeX is available, produces a clean PDF after verification passes.

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Use when an RFP, RFI, RFQ, security questionnaire, vendor questionnaire, or proposal request arrives and the team needs a structured response — parsing multi-section buyer-dictated requirements (MANDATORY vs WEIGHTED vs NICE-TO-HAVE), building a Shipley-method proof-point matrix mapping each requirement to a verifiable proof point, articulating 3-5 win-themes that ladder up across requirements, and producing a Shipley-derived winrate estimate that informs a bid / no-bid / partner-bid recommendation. For Bid Managers, Proposal Leads, Directors of Sales, and Sales Engineers at the response-strategy moment. Surfaces GAP requirements explicitly — never invents claims. NOT free-form proposal narrative authoring, NOT contract redline, NOT marketing collateral.

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Develop and verify a mathematical proof in Lean, continue an incomplete Lean project, or audit whether it proves the original statement. Connect actual inputs to intermediate lemmas, assemble the target theorem, check its transitive axioms, and provide a reproducible handoff. Use when Lean is requested or a specific proof obligation benefits from formal verification; use proof-writer for ordinary mathematical drafting.

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create a fraimz, make fraimz, prove it works, frame proof, PR proof, validate experience, e2e evidence, fraimz.html. The full fraimz loop — frame the claim, drive the real app via CDP, validate/repair, output fraimz.html. Use whenever a task ends with "please create a fraimz" or any change needs end-to-end proof.

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do e2e tests, run e2e, validate feature, prove it works, PR proof, frame proof, pnpm evals. Launches iPolloWork on Daytona or local Electron and runs the coded eval flows via CDP. Launch + run mechanics; the proof loop itself is the fraimz skill.

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Use when the user asks to "build our pitch deck narrative", "write a fundraising story", or "structure the sales pitch narrative"; derives from the narrative canon a company pitch/deck narrative — problem → the undeniable shift → product-as-hero → proof → the ask — as a slide-beat outline (one narrative beat per slide, with the claim ID each proof beat rests on), for both a sales pitch and a fundraising deck. Every proof beat is labeled Measured / User-provided / '[needs source]' and unverified ones route to the claims candidates. Not for the launch-window battle cards and talk track — use sales-enablement-kit; not for the durable message hierarchy or the arc itself — use message-system-architect / strategic-narrative-designer; not for finished deck visual design — out of scope; not for claim adjudication — use offer-claims-registry. 路演叙事/融资故事/销售 pitch/幻灯节拍

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Plan and collect OpenClaw Windows validation/proof: tests, rubber-duck review, UI evidence, MCP output, and gateway runtime proof.

日本語の概要は準備中です。原文の説明を表示しています。

Read-only proofreading pass over lecture `.tex` or `.qmd` files. Checks grammar, typos, overflow, terminology consistency, and academic writing quality; produces a report without editing. Use when user says "proofread", "check for typos", "look for grammar issues", "copy-edit this", "any writing errors?", or before a lecture release.

日本語の概要は準備中です。原文の説明を表示しています。