Thm* a:T, Q:(T Prop). (a = !x:T. Q(x))  a {!x:T | Q(x)} | [uni_sat_imp_in_uni_set] |
Thm* (P  Q)  (Q  P)  (P  Q) | [implies_antisymmetry] |
Thm* (P  Q)  ( P  Q) | [squash_functionality_wrt_iff] |
Thm* (P  Q)  P  Q | [squash_functionality_wrt_implies] |
Thm* (P1  P2)  (Q1  Q2)  P1 Q1  P2 Q2 | [or_functionality_wrt_implies] |
Thm* (P1  P2)  (Q1  Q2)  (P1 Q1  P2 Q2) | [or_functionality_wrt_iff] |
Thm* (P  Q)  P  Q | [not_functionality_wrt_implies] |
Thm* (P  Q)  ( P  Q) | [not_functionality_wrt_iff] |
Thm* P,Q:(S Prop).
Thm* S = T  ( x:S. P(x)  Q(x))  ( x:S. P(x))  ( y:T. Q(y)) | [exists_functionality_wrt_implies] |
Thm* P,Q:(S Prop).
Thm* S = T  ( x:S. P(x)  Q(x))  (( x:S. P(x))  ( y:T. Q(y))) | [exists_functionality_wrt_iff] |
Thm* P,Q:(S Prop).
Thm* S = T  ( z:S. P(z)  Q(z))  ( x:S. P(x))  ( y:T. Q(y)) | [all_functionality_wrt_implies] |
Thm* P,Q:(S Prop).
Thm* S = T  ( x:S. P(x)  Q(x))  (( x:S. P(x))  ( y:T. Q(y))) | [all_functionality_wrt_iff] |
Thm* (P1  P2)  (Q1  Q2)  ((P1  Q1)  (P2  Q2)) | [iff_functionality_wrt_iff] |
Thm* (P  Q)  (Dec(P)  Dec(Q)) | [decidable_functionality] |
Thm* (P1  P2)  (Q1  Q2)  (P1  Q1)  P2  Q2 | [implies_functionality_wrt_implies] |
Thm* (P1  P2)  (Q1  Q2)  ((P1  Q1)  (P2  Q2)) | [implies_functionality_wrt_iff] |
Thm* (P1  P2)  (Q1  Q2)  P1 & Q1  P2 & Q2 | [and_functionality_wrt_implies] |
Thm* (P1  P2)  (Q1  Q2)  (P1 & Q1  P2 & Q2) | [and_functionality_wrt_iff] |
Thm* (P  Q)  (Q  R)  P  R | [implies_transitivity] |
Thm* (P  Q)  (Q  R)  (P  R) | [iff_transitivity] |
Thm* Dec(A)  ( (A & B)  A B) | [not_over_and] |
Thm* A B  (A & B) | [not_over_and_b] |
Thm* Dec(A)  ( A  A) | [dneg_elim_a] |
Thm* Dec(A)   A  A | [dneg_elim] |
Thm* SqStable(P)  ( P  P) | [squash_elim] |
Thm* Dec(P)  SqStable(P) | [sq_stable_from_decidable] |
Thm* Stable{P}  SqStable(P) | [sq_stable__from_stable] |
Thm* P:(A Prop). ( x:A. SqStable(P(x)))  SqStable( x:A. P(x)) | [sq_stable__all] |
Thm* SqStable(P)  SqStable(Q)  SqStable(P  Q) | [sq_stable__iff] |
Thm* SqStable(Q)  SqStable(P  Q) | [sq_stable__implies] |
Thm* SqStable(P)  SqStable(Q)  SqStable(P & Q) | [sq_stable__and] |
Thm* Dec(P)  Stable{P} | [stable__from_decidable] |
Thm* f,g:(A B). ( x:A. Stable{f(x) = g(x)})  Stable{f = g} | [stable__function_equal] |
Thm* Dec(A)  (A  B)  Dec(B) | [iff_preserves_decidability] |
Thm* Dec(P)  Dec(Q)  Dec(P  Q) | [decidable__iff] |
Thm* Dec(P)  Dec(Q)  Dec(P  Q) | [decidable__implies] |
Thm* Dec(P)  Dec(Q)  Dec(P & Q) | [decidable__and] |
Thm* Dec(P)  Dec(Q)  Dec(P Q) | [decidable__or] |
Def a = !x:T. Q(x) == Q(a) & ( a':T. Q(a')  a' = a) | [uni_sat] |
Def {!x:T | P(x)} == {x:T| P(x) & ( y:T. P(y)  y = x) } | [unique_set] |
Def SqStable(P) == P  P | [sq_stable] |
Def Stable{P} ==  P  P | [stable] |
Def P  Q == (P  Q) & (P  Q) | [iff] |
Def A == A  False | [not] |
Def P  Q == Q  P | [rev_implies] |