Nuprl Lemma : fpf-compatible-join-cap
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[f,g:a:A fp-> B[a]]. ∀[x:A]. ∀[z:B[x]].
f ⊕ g(x)?z = g(x)?f(x)?z ∈ B[x] supposing f || g
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-compatible: f || g,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
fpf-compatible_wf,
fpf_wf,
deq_wf,
fpf-dom_wf,
fpf-join_wf,
top_wf,
subtype-fpf2,
subtype_top,
bool_wf,
fpf-join-dom,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
fpf-join-ap-left,
fpf-ap_wf,
iff_weakening_equal,
or_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf-join-ap-sq
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f,g:a:A fp-> B[a]]. \mforall{}[x:A]. \mforall{}[z:B[x]].
f \moplus{} g(x)?z = g(x)?f(x)?z supposing f || g
Date html generated:
2015_07_17-AM-11_13_31
Last ObjectModification:
2015_02_04-PM-05_05_59
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