Nuprl Lemma : fpf-join-ap-left
∀[A:Type]. ∀[B,C:A ─→ Type]. ∀[eq:EqDecider(A)]. ∀[f:a:A fp-> B[a]]. ∀[g:a:A fp-> C[a]]. ∀[x:A].
f ⊕ g(x) = f(x) ∈ B[x] supposing ↑x ∈ dom(f)
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
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 :
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
fpf_wf,
deq_wf,
bool_wf,
fpf-ap_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[A:Type]. \mforall{}[B,C:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[g:a:A fp-> C[a]]. \mforall{}[x:A].
f \moplus{} g(x) = f(x) supposing \muparrow{}x \mmember{} dom(f)
Date html generated:
2015_07_17-AM-09_20_03
Last ObjectModification:
2015_01_28-AM-07_48_46
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