Nuprl Lemma : fpf-union-compatible_symmetry
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[C:Type].
∀eq:EqDecider(A). ∀f,g:x:A fp-> B[x] List. ∀R:(C List) ⟶ C ⟶ 𝔹.
(fpf-union-compatible(A;C;x.B[x];eq;R;f;g) ⇒ fpf-union-compatible(A;C;x.B[x];eq;R;g;f))
supposing ∀a:A. (B[a] ⊆r C)
Proof
Definitions occuring in Statement :
fpf-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g),
fpf: a:A fp-> B[a],
list: T List,
deq: EqDecider(T),
bool: 𝔹,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
fpf-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g),
or: P ∨ Q,
and: P ∧ Q,
guard: {T},
cand: A c∧ B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
top: Top
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[C:Type].
\mforall{}eq:EqDecider(A). \mforall{}f,g:x:A fp-> B[x] List. \mforall{}R:(C List) {}\mrightarrow{} C {}\mrightarrow{} \mBbbB{}.
(fpf-union-compatible(A;C;x.B[x];eq;R;f;g) {}\mRightarrow{} fpf-union-compatible(A;C;x.B[x];eq;R;g;f))
supposing \mforall{}a:A. (B[a] \msubseteq{}r C)
Date html generated:
2016_05_16-AM-11_05_35
Last ObjectModification:
2015_12_29-AM-09_14_09
Theory : event-ordering
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