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Mirrors > Home > HOLE Home > Th. List > hbl | GIF version |
Description: Hypothesis builder for lambda abstraction. |
Ref | Expression |
---|---|
hbl.1 | ⊢ A:γ |
hbl.2 | ⊢ B:α |
hbl.3 | ⊢ R⊧[(λx:α AB) = A] |
Ref | Expression |
---|---|
hbl | ⊢ R⊧[(λx:α λy:β AB) = λy:β A] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbl.1 | . . . . 5 ⊢ A:γ | |
2 | 1 | wl 59 | . . . 4 ⊢ λy:β A:(β → γ) |
3 | 2 | wl 59 | . . 3 ⊢ λx:α λy:β A:(α → (β → γ)) |
4 | hbl.2 | . . 3 ⊢ B:α | |
5 | 3, 4 | wc 45 | . 2 ⊢ (λx:α λy:β AB):(β → γ) |
6 | hbl.3 | . . . 4 ⊢ R⊧[(λx:α AB) = A] | |
7 | 6 | ax-cb1 29 | . . 3 ⊢ R:∗ |
8 | 1, 4 | distrl 84 | . . 3 ⊢ ⊤⊧[(λx:α λy:β AB) = λy:β (λx:α AB)] |
9 | 7, 8 | a1i 28 | . 2 ⊢ R⊧[(λx:α λy:β AB) = λy:β (λx:α AB)] |
10 | 1 | wl 59 | . . . 4 ⊢ λx:α A:(α → γ) |
11 | 10, 4 | wc 45 | . . 3 ⊢ (λx:α AB):γ |
12 | 11, 6 | leq 81 | . 2 ⊢ R⊧[λy:β (λx:α AB) = λy:β A] |
13 | 5, 9, 12 | eqtri 85 | 1 ⊢ R⊧[(λx:α λy:β AB) = λy:β A] |
Colors of variables: type var term |
Syntax hints: → ht 2 kc 5 λkl 6 = ke 7 [kbr 9 ⊧wffMMJ2 11 wffMMJ2t 12 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ceq 46 ax-leq 62 ax-distrl 63 |
This theorem depends on definitions: df-ov 65 |
This theorem is referenced by: cbvf 167 ax7 196 axrep 207 |
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