Present — what is happening now, and what happens habitually
| yo | demuestroI prove | nosotros | demostramoswe prove |
| tú | demuestrasyou prove | vosotros | demostráisyou all prove |
| él/ella/Ud. | demuestrahe/she proves | ellos/Uds. | demuestranthey prove |
Present perfect — have —ed; a past still touching now. Spain: today, this week. Latin America: mostly the indefinido instead
| yo | he demostradoI have proved | nosotros | hemos demostradowe have proved |
| tú | has demostradoyou have proved | vosotros | habéis demostradoyou all have proved |
| él/ella/Ud. | ha demostradohe/she has proved | ellos/Uds. | han demostradothey have proved |
Present subjunctive — after que with wishes, doubt, emotion, ojalá
| yo | demuestre(that) I prove | nosotros | demostremos(that) we prove |
| tú | demuestres(that) you prove | vosotros | demostréis(that) you all prove |
| él/ella/Ud. | demuestre(that) he/she proves | ellos/Uds. | demuestren(that) they prove |
Present perfect subjunctive — have —ed, under doubt or emotion: no creo que haya venido
| yo | haya demostrado(that) I have proved | nosotros | hayamos demostrado(that) we have proved |
| tú | hayas demostrado(that) you have proved | vosotros | hayáis demostrado(that) you all have proved |
| él/ella/Ud. | haya demostrado(that) he/she has proved | ellos/Uds. | hayan demostrado(that) they have proved |
Preterite — a finished past action — it started, it ended
| yo | demostréI proved | nosotros | demostramoswe proved |
| tú | demostrasteyou proved | vosotros | demostrasteisyou all proved |
| él/ella/Ud. | demostróhe/she proved | ellos/Uds. | demostraronthey proved |
Imperfect — used to / was —ing; background, habits, descriptions
| yo | demostrabaI used to prove | nosotros | demostrábamoswe used to prove |
| tú | demostrabasyou used to prove | vosotros | demostrabaisyou all used to prove |
| él/ella/Ud. | demostrabahe/she used to prove | ellos/Uds. | demostrabanthey used to prove |
Past perfect — had —ed; further back than another past event
| yo | había demostradoI had proved | nosotros | habíamos demostradowe had proved |
| tú | habías demostradoyou had proved | vosotros | habíais demostradoyou all had proved |
| él/ella/Ud. | había demostradohe/she had proved | ellos/Uds. | habían demostradothey had proved |
Imperfect subjunctive — si clauses and past-tense wishes: si tuviera, quería que fuera
| yo | demostrara(that) I proved | nosotros | demostráramos(that) we proved |
| tú | demostraras(that) you proved | vosotros | demostrarais(that) you all proved |
| él/ella/Ud. | demostrara(that) he/she proved | ellos/Uds. | demostraran(that) they proved |
Imperfect subjunctive — the same tense, second form; commoner in Spain and in writing
| yo | demostrase(that) I proved | nosotros | demostrásemos(that) we proved |
| tú | demostrases(that) you proved | vosotros | demostraseis(that) you all proved |
| él/ella/Ud. | demostrase(that) he/she proved | ellos/Uds. | demostrasen(that) they proved |
Past perfect subjunctive — had —ed, hypothetically: si hubiera sabido
| yo | hubiera demostrado(that) I had proved | nosotros | hubiéramos demostrado(that) we had proved |
| tú | hubieras demostrado(that) you had proved | vosotros | hubierais demostrado(that) you all had proved |
| él/ella/Ud. | hubiera demostrado(that) he/she had proved | ellos/Uds. | hubieran demostrado(that) they had proved |
Preterite perfect — had —ed, immediately before; literary, all but extinct
| yo | hube demostradoI had proved | nosotros | hubimos demostradowe had proved |
| tú | hubiste demostradoyou had proved | vosotros | hubisteis demostradoyou all had proved |
| él/ella/Ud. | hubo demostradohe/she had proved | ellos/Uds. | hubieron demostradothey had proved |
Future — will — (spoken Spanish often prefers voy a + infinitivo)
| yo | demostraréI will prove | nosotros | demostraremoswe will prove |
| tú | demostrarásyou will prove | vosotros | demostraréisyou all will prove |
| él/ella/Ud. | demostraráhe/she will prove | ellos/Uds. | demostraránthey will prove |
Conditional — would —; also softens a request into politeness
| yo | demostraríaI would prove | nosotros | demostraríamoswe would prove |
| tú | demostraríasyou would prove | vosotros | demostraríaisyou all would prove |
| él/ella/Ud. | demostraríahe/she would prove | ellos/Uds. | demostraríanthey would prove |
Future perfect — will have —ed; done by some future point
| yo | habré demostradoI will have proved | nosotros | habremos demostradowe will have proved |
| tú | habrás demostradoyou will have proved | vosotros | habréis demostradoyou all will have proved |
| él/ella/Ud. | habrá demostradohe/she will have proved | ellos/Uds. | habrán demostradothey will have proved |
Conditional perfect — would have —ed; the road not taken
| yo | habría demostradoI would have proved | nosotros | habríamos demostradowe would have proved |
| tú | habrías demostradoyou would have proved | vosotros | habríais demostradoyou all would have proved |
| él/ella/Ud. | habría demostradohe/she would have proved | ellos/Uds. | habrían demostradothey would have proved |
Future subjunctive — legal and proverbial only: adonde fueres, haz lo que vieres
| yo | demostrare(should) I prove | nosotros | demostráremos(should) we prove |
| tú | demostrares(should) you prove | vosotros | demostrareis(should) you all prove |
| él/ella/Ud. | demostrare(should) he/she prove | ellos/Uds. | demostraren(should) they prove |
Imperative (do it) — orders and requests; there is no yo form
| yo | — | nosotros | demostremoslet's prove |
| tú | demuestraprove! | vosotros | demostradprove! |
| él/ella/Ud. | demuestreprove! | ellos/Uds. | demuestrenprove! |
Imperative (don't) — no + subjunctive — never the affirmative form with no in front
| yo | — | nosotros | no demostremoslet's not prove |
| tú | no demuestresdon't prove | vosotros | no demostréisdon't prove |
| él/ella/Ud. | no demuestredon't prove | ellos/Uds. | no demuestrendon't prove |

Red = the form breaks the regular pattern. Everything in black you could have worked out from the endings alone.
I — the speaker
| Presente | demuestroI prove |
| Perfecto | he demostradoI have proved |
| Subj. presente | demuestre(that) I prove |
| Subj. perfecto | haya demostrado(that) I have proved |
| Futuro | demostraréI will prove |
| Condicional | demostraríaI would prove |
| Fut. perfecto | habré demostradoI will have proved |
| Cond. perfecto | habría demostradoI would have proved |
| Subj. futuro | demostrare(should) I prove |
| Indefinido | demostréI proved |
| Imperfecto | demostrabaI used to prove |
| Pluscuamp. | había demostradoI had proved |
| Subj. imperf. | demostrara(that) I proved |
| Subj. -se | demostrase(that) I proved |
| Subj. pluscuamp. | hubiera demostrado(that) I had proved |
| Pret. anterior | hube demostradoI had proved |
| Imperativo | — |
| Imper. negativo | — |
we — the speaker plus others
| Presente | demostramoswe prove |
| Perfecto | hemos demostradowe have proved |
| Subj. presente | demostremos(that) we prove |
| Subj. perfecto | hayamos demostrado(that) we have proved |
| Futuro | demostraremoswe will prove |
| Condicional | demostraríamoswe would prove |
| Fut. perfecto | habremos demostradowe will have proved |
| Cond. perfecto | habríamos demostradowe would have proved |
| Subj. futuro | demostráremos(should) we prove |
| Indefinido | demostramoswe proved |
| Imperfecto | demostrábamoswe used to prove |
| Pluscuamp. | habíamos demostradowe had proved |
| Subj. imperf. | demostráramos(that) we proved |
| Subj. -se | demostrásemos(that) we proved |
| Subj. pluscuamp. | hubiéramos demostrado(that) we had proved |
| Pret. anterior | hubimos demostradowe had proved |
| Imperativo | demostremoslet's prove |
| Imper. negativo | no demostremoslet's not prove |
you (informal) — one person you are familiar with
| Presente | demuestrasyou prove |
| Perfecto | has demostradoyou have proved |
| Subj. presente | demuestres(that) you prove |
| Subj. perfecto | hayas demostrado(that) you have proved |
| Futuro | demostrarásyou will prove |
| Condicional | demostraríasyou would prove |
| Fut. perfecto | habrás demostradoyou will have proved |
| Cond. perfecto | habrías demostradoyou would have proved |
| Subj. futuro | demostrares(should) you prove |
| Indefinido | demostrasteyou proved |
| Imperfecto | demostrabasyou used to prove |
| Pluscuamp. | habías demostradoyou had proved |
| Subj. imperf. | demostraras(that) you proved |
| Subj. -se | demostrases(that) you proved |
| Subj. pluscuamp. | hubieras demostrado(that) you had proved |
| Pret. anterior | hubiste demostradoyou had proved |
| Imperativo | demuestraprove! |
| Imper. negativo | no demuestresdon't prove |
you all — informal plural, Spain only
| Presente | demostráisyou all prove |
| Perfecto | habéis demostradoyou all have proved |
| Subj. presente | demostréis(that) you all prove |
| Subj. perfecto | hayáis demostrado(that) you all have proved |
| Futuro | demostraréisyou all will prove |
| Condicional | demostraríaisyou all would prove |
| Fut. perfecto | habréis demostradoyou all will have proved |
| Cond. perfecto | habríais demostradoyou all would have proved |
| Subj. futuro | demostrareis(should) you all prove |
| Indefinido | demostrasteisyou all proved |
| Imperfecto | demostrabaisyou all used to prove |
| Pluscuamp. | habíais demostradoyou all had proved |
| Subj. imperf. | demostrarais(that) you all proved |
| Subj. -se | demostraseis(that) you all proved |
| Subj. pluscuamp. | hubierais demostrado(that) you all had proved |
| Pret. anterior | hubisteis demostradoyou all had proved |
| Imperativo | demostradprove! |
| Imper. negativo | no demostréisdon't prove |
he, she, you (formal) — one other person — formal you shares it
| Presente | demuestrahe/she proves |
| Perfecto | ha demostradohe/she has proved |
| Subj. presente | demuestre(that) he/she proves |
| Subj. perfecto | haya demostrado(that) he/she has proved |
| Futuro | demostraráhe/she will prove |
| Condicional | demostraríahe/she would prove |
| Fut. perfecto | habrá demostradohe/she will have proved |
| Cond. perfecto | habría demostradohe/she would have proved |
| Subj. futuro | demostrare(should) he/she prove |
| Indefinido | demostróhe/she proved |
| Imperfecto | demostrabahe/she used to prove |
| Pluscuamp. | había demostradohe/she had proved |
| Subj. imperf. | demostrara(that) he/she proved |
| Subj. -se | demostrase(that) he/she proved |
| Subj. pluscuamp. | hubiera demostrado(that) he/she had proved |
| Pret. anterior | hubo demostradohe/she had proved |
| Imperativo | demuestreprove! |
| Imper. negativo | no demuestredon't prove |
they, you all — several others — plural you shares it
| Presente | demuestranthey prove |
| Perfecto | han demostradothey have proved |
| Subj. presente | demuestren(that) they prove |
| Subj. perfecto | hayan demostrado(that) they have proved |
| Futuro | demostraránthey will prove |
| Condicional | demostraríanthey would prove |
| Fut. perfecto | habrán demostradothey will have proved |
| Cond. perfecto | habrían demostradothey would have proved |
| Subj. futuro | demostraren(should) they prove |
| Indefinido | demostraronthey proved |
| Imperfecto | demostrabanthey used to prove |
| Pluscuamp. | habían demostradothey had proved |
| Subj. imperf. | demostraran(that) they proved |
| Subj. -se | demostrasen(that) they proved |
| Subj. pluscuamp. | hubieran demostrado(that) they had proved |
| Pret. anterior | hubieron demostradothey had proved |
| Imperativo | demuestrenprove! |
| Imper. negativo | no demuestrendon't prove |

Red = the form breaks the regular pattern. Everything in black you could have worked out from the endings alone.